Project parts and some of the solutions by eCLWQc

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									PATRICIA FULLER                                          10/31/2010 11:52 AM

                                                                                               [Hide
                                                                                            comments]
                                                                                            Rounding
                                                                                            error in
                                                                                            p(orange)s/b
                                                                                            .2162 (-1
                                                                                            point)
                                                                                            Rounding
                                                                                            precision in
                                                                                            Sample
                                                                                            mean (4-6
  Rounding error in p(orange)s/b .2162 (-1 point) Rounding precision in Sample mean (4-6    Decimal
De …                                                                                        places) (-1
                                                                                            point)
                                                                                            Error in
                                                                                            Sample
                                                                                            Standard
                                                                                            Deviation
                                                                                            s/b 1.9708
                                                                                            (-1 pt)
                                                                                            Written
                                                                                            Description
                                                                                            of Histogram
                                                                                            (-1 point)

PATRICIA FULLER                                          10/29/2010 8:08 PM

                                                                                               [Hide
                                                                                            comments]
                                                                                            Rounding
                                                                                            error in
                                                                                            p(orange)s/b
                                                                                            .2162 (-1
                                                                                            point)
                                                                                            Rounding
                                                                                            precision in
                                                                                            Sample
                                                                                            mean (4-6
 Rounding error in p(orange)s/b .2162 (-1 point) Rounding precision in Sample mean (4-6     Decimal
D…                                                                                          places) (-1
                                                                                            point)
                                                                                            Error in
                                                                                            Sample
                                                                                            Standard
                                                                                            Deviation
                                                                                            s/b 1.9708
                                                                                            (-1 pt)
                                                                                            Written
                                                                                            Description
                                                                                            of Histogram
                                                                                            (-1 point)

VANESSA HENDERSON-ROLLE                                  10/24/2010 9:34 PM

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                                                                                            comments]
  Good Evening Professor, Please find the attached M&M Project Part II for your review. …   Good
                                                                                            Evening
                                                                                            Professor,
                                                                                                 Please find
                                                                                                 the attached
                                                                                                 M&M Project
                                                                                                 Part II for
                                                                                                 your
                                                                                                 review.
                                                                                                 Thank You!

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PATRICIA FULLER                                             11/17/2010 9:26 PM

                                                                                                     [Hide
                                                                                                  comments]
                                                                                                  It looks
                                                                                                  like you
                                                                                                  copied the
                                                                                                  Green
                                                                                                  results for
                                                                                                  the Orange
                                                                                                  line (-3)
                                                                                                  What is
                                                                                                  #7?
                                                                                                  The
                                                                                                  Confidence
                                                                                                  interval
  It looks like you copied the Green results for the Orange line (-3) What is #7? The Confid …    pasted
                                                                                                  from
                                                                                                  StatCrunch
                                                                                                  is correct
                                                                                                  for the C.I.
                                                                                                  of the
                                                                                                  mean.
                                                                                                  Your bonus
                                                                                                  is
                                                                                                  incorrect.
                                                                                                  Use the
                                                                                                  formula
                                                                                                  from page
                                                                                                  338 in the
                                                                                                  text.

PATRICIA FULLER                                             11/17/2010 9:01 PM

                                                                                                     [Hide
                                                                                                  comments]
                                                                                                  It looks
                                                                                                  like you
                                                                                                  copied the
  It looks like you copied the Green results for the Orange line (-3) What is #7? The Conf …      Green
                                                                                                  results for
                                                                                                  the Orange
                                                                                                  line (-3)
                                                                                                  What is
                                                                                                  #7?
                                                                                                 The
                                                                                                 Confidence
                                                                                                 interval
                                                                                                 pasted
                                                                                                 from
                                                                                                 StatCrunch
                                                                                                 is correct
                                                                                                 for the C.I.
                                                                                                 of the
                                                                                                 mean.
                                                                                                 Your bonus
                                                                                                 is
                                                                                                 incorrect.
                                                                                                 Use the
                                                                                                 formula
                                                                                                 from page
                                                                                                 338 in the
                                                                                                 text.

VANESSA HENDERSON-ROLLE                                      11/14/2010 7:18 PM

                                                                                                    [Hide
                                                                                                 comments]
                                                                                                 Hello
                                                                                                 Professor,
                                                                                                 Please find
                                                                                                 the
                                                                                                 attached
    Hello Professor, Please find the attached M&M Project Part 3, with an attempt to complete    M&M
…                                                                                                Project
                                                                                                 Part 3,
                                                                                                 with an
                                                                                                 attempt to
                                                                                                 complete
                                                                                                 the bonus
                                                                                                 question.
                                                                                                 Thanks!

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PATRICIA FULLER                                           12/1/2010 10:00 PM

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                                                                                             comments]
                                                                                             Everything is
                                                                                             great, except
                                                                                             for the
                                                                                             conclusion. You
  Everything is great, except for the conclusion. You should bring in a short statement of   should bring in
what …                                                                                       a short
                                                                                             statement of
                                                                                             what that
                                                                                             means in
                                                                                             relationship to
                                                                                             the scenario (-
                                                                                             .5 point)

VANESSA HENDERSON-ROLLE                                   11/28/2010 5:40 PM
Hello Professor, Please find the attached M&M Project for

PATRICIA FULLER                                         12/20/2010 6:43 PM

                                                                                         [Hide
                                                                                      comments]
                                                                                      I agree, it was
                                                                                      difficult to narrow
                                                                                      down - no student
                                                                                      submitted a paper
                                                                                      of only 3 pages
                                                                                      (including yours,
                                                                                      which was 5
                                                                                      pages).
                                                                                      I don't
                                                                                      understand what
                                                                                      you mean by your
                                                                                      analysis of
  I agree, it was difficult to narrow down - no student submitted a paper of only 3
                                                                                      standard
pages (including y …
                                                                                      deviation. I do not
                                                                                      find any
                                                                                      explanations of
                                                                                      the terminology,
                                                                                      nor did I find any
                                                                                      explanation of a
                                                                                      way to investigate
                                                                                      the unexpected
                                                                                      results.
                                                                                      If you would like
                                                                                      to revise and
                                                                                      resubmit, I will
                                                                                      regrade this
                                                                                      project.

PATRICIA FULLER                                         12/18/2010 1:54 PM

                                                                                         [Hide
                                                                                      comments]
                                                                                      I agree, it was
                                                                                      difficult to narrow
                                                                                      down - no student
                                                                                      submitted a paper
                                                                                      of only 3 pages
                                                                                      (including yours,
                                                                                      which was 5
                                                                                      pages).
                                                                                      I don't
  I agree, it was difficult to narrow down - no student submitted a paper of only 3   understand what
pages (including y …                                                                  you mean by your
                                                                                      analysis of
                                                                                      standard
                                                                                      deviation. I do not
                                                                                      find any
                                                                                      explanations of
                                                                                      the terminology,
                                                                                      nor did I find any
                                                                                      explanation of a
                                                                                      way to investigate
                                                                                      the unexpected
                                                                                      results.
                                                                                      If you would like
                                                                                       to revise and
                                                                                       resubmit, I will
                                                                                       regrade this
                                                                                       project.

VANESSA HENDERSON-ROLLE                                12/16/2010 6:21 AM

                                                                                          [Hide
                                                                                       comments]
                                                                                       Professor thanks
                                                                                       for your
                                                                                       feedback. This
                                                                                       was a difficult
                                                                                       report to narrow
                                                                                       now and
                                                                                       articulate in 3
                                                                                       pages. I actually
                                                                                       cut out a lot to
                                                                                       show the analysis,
                                                                                       however I did
                                                                                       indicate the
                                                                                       rationale as to
                                                                                       what I believed to
                                                                                       be my analysis for
                                                                                       the standard
                                                                                       deviation. store
   Professor thanks for your feedback. This was a difficult report to narrow now and
                                                                                       locations,
articulate i …
                                                                                       unknown factors
                                                                                       based on students
                                                                                       testing methods
                                                                                       and validity and
                                                                                       production which
                                                                                       were not
                                                                                       monitored or
                                                                                       controlled as a
                                                                                       part of this study.
                                                                                       (paragraph 1)
                                                                                       Please advise and
                                                                                       consider these
                                                                                       components in
                                                                                       your final
                                                                                       grading. I will
                                                                                       check back
                                                                                       today. Thanks for
                                                                                       your
                                                                                       consideration.

PATRICIA FULLER                                        12/15/2010 7:15 PM

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                                                                                       comments]
                                                                                           1.
                                                                                           Present the
                                                                                           methods,
                                                                                           analysis and
  1.      Present the methods, analysis and results for the …
                                                                                           results for
                                                                                           the five parts
                                                                                           of the
                                                                                           project. (30
                                                                                           points)
                                                                                           2.
                                                                                          Explain how
                                                                                          to
                                                                                          investigate
                                                                                          unexpected
                                                                                          results
                                                                                          (failed tests
                                                                                          in Part 4)
                                                                                          and
                                                                                          speculate on
                                                                                          at least three
                                                                                          plausible
                                                                                          causes for
                                                                                          the observed
                                                                                          results You
                                                                                          did not
                                                                                          suggest any
                                                                                          possible
                                                                                          causes for
                                                                                          the
                                                                                          unexpected
                                                                                          results. (0
                                                                                          points)
                                                                                          3.
                                                                                          Clarity:
                                                                                          Explain all
                                                                                          statistical
                                                                                          terminology
                                                                                          in every-day
                                                                                          language.
                                                                                           You did not
                                                                                          attempt to
                                                                                          define any
                                                                                          of the
                                                                                          terminology
                                                                                          in every
                                                                                          day
                                                                                          language.
                                                                                          (0 points)
                                                                                          4.
                                                                                          Writing :
                                                                                          Grammar,
                                                                                          sentence
                                                                                          structure,
                                                                                          paragraph
                                                                                          structure,
                                                                                          spelling,
                                                                                          punctuation,
                                                                                          APA usage.
                                                                                          (30 points)


VANESSA HENDERSON-ROLLE                              12/5/2010 9:07 PM

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                                                                                      comments]
  Good Day Professor, Please find the attached M&M Project Report attached for your
review.& …                                                                            Good Day
                                                                                      Professor, Please
                                                                                      find the attached
                                                                                   M&M Project
                                                                                   Report attached
                                                                                   for your review.
                                                                                   Thank You.

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                                             MAT 300
                                          m&ms® Project
                                           Part 1 (10 pts)

Throughout this course we will be using m&ms® data to help explain some of the concepts
being taught as well as give you a feel for how these methods can be used. We will be exploring
plain m&ms® and I have chosen to use the 1.69 oz size bags for convenience and affordability.
From a larger perspective, the purpose of our report is to examine the packaging process for
plain 1.69 ounce bags of m&ms®.

In order to get started, everyone needs to visit three (3) different stores and purchase a plain
m&ms® 1.69 oz bag of candy. It is not necessary to keep track of which bag came from which
store. Why do we need to do this? We are taking a sample of the population of all 1.69 oz bags
of plain m&ms® that are produced. In order for our results to be meaningful, we need a random
sample. Random samples are found by sampling at complete and total random. By visiting three
different stores and then randomly selecting a bag from the display, we are assuring that we are
obtaining a true random sample. Other sampling methods will also produce a random sample.
The concepts of population, sample, and sampling methods will be explained further in Chapter
1.

Download the mnminput.xls file found in doc sharing. Once you have your three bags, you will
need to open each one individually and record the number of candies of each color within the
bag (blue, orange, green, yellow, red, and brown) into the file. Once you have done this for each
bag, save the file and place it into the Part 1 dropbox in eCollege.

Here is the best part of the project. When you are done counting the colors and recording your
data, feel free to enjoy the candy!

Please note that everyone’s data will be combined into ONE class data set. This data set will be
used for all the remaining parts of the project. There will be an announcement when the class
data set has been uploaded to Doc Sharing. Because we are only sampling 1.69 oz bags, all our
conclusions will be based upon plain 1.69 oz bags of m&ms®. We will be focusing on the
overall percentage of each color and the total number of candies per bag.

At the end of the project, you will be writing a summary of all parts of the project. It will be
written as a formal report to a supervisor or manager. More information will be given.


                                             MAT 300
                                        M&Ms® Project
                                         Part 2 (30 pts)

Use the Excel data file found in the doc sharing area (mnmproject.xls) to complete this
assignment. If using Excel 2003, you will want to go to Tools > Add-Ins and make sure the
boxes to the left of both analysis toolpaks are checked as we will be using those tools throughout
the term. If using Excel 2007, you will click on the Microsoft Office Button in the upper left,
then click “Excel Options”. Click on Add-Ins, then in the Manage box, select Excel Add-Ins.
Click Go. In the “Add-Ins available box, select the Analysis ToolPak check box and then “Ok”.
Please refer to the sample project file (samplemnmpart2.xls) in the Doc Sharing area for an
example of what your completed file will look like if you follow all the outlined steps. Be sure
to submit your Excel file into the dropbox.

From this point forward, we will be focusing on the data from two perspectives: color
proportions and the number of candies per bag. For the color proportions, the information that
will be used is the total for each color and the total number of candies sampled. For the number
of candies per bag, you will use the data in the num. candies in bag column.

18 pts (3 for each color). Add up each of the columns. Calculate the sample proportions ( ) for
each of the colors. For example, the sample proportion of blue candies would be the total
number of blue candies from all the bags divided by the total number of candies in all the bags.

3 pts. Calculate the sample mean ( ) number of candies per 1.69 oz bag. (Find the mean of the
number of candies in bag column).

3 pts. In another sheet in the Excel data file, create a histogram for the number of candies per
bag. To do this in Excel 2003, go to Tools in the menu and click on Data Analysis, then select
Histogram. In Excel 2007, select the Data tab and then click on Data Analysis in the Analysis
box. Click in the input range and then select the column containing the total number of candies
per bag. Be careful that you do not include the cell that has the total for the column. Select the
bin column on the data page for bin range. The “bin” column tells Excel how to group the data
into classes for graphing. If you include the cell with the labels (total and bin) when selecting
the cells, be sure the box next to Labels is checked. Under output options, select the new
worksheet ply and name it Histogram. Check next to Chart output. Finally click ok, and the
histogram will be within the new worksheet page. If you will click and hold on the square in the
bottom center of the histogram chart, then move the mouse down, you can widen the chart and
make it easier to read.

If you do not have the Analysis toolpak in Excel, you can use StatCrunch to do this part. A link
to StatCrunch can be found under the Tools for Success, the webliography and on each
homework and MML quiz problem. Copy the “number of candies in bag” column into
StatCrunch. To do this, you will copy the column in Excel including the column header (num.
candies in bag). Then after opening StatCrunch, you will select Data > Load Data > from paste.
In the window that opens, click on “paste data from clipboard”, then click “okay”. The data will
be loaded into StatCrunch. Next select Graphics > Histogram. In the popup window, select the
name of the column that contains your data, click next. Next, enter 1 in the box to the right of
“binwidth”, then click “Create Graph!” The output can be copied and pasted into your Excel
file.

3 pts. In another sheet in the file, use Excel to compute the descriptive statistics for the total
number of candies per bag. This data includes sample mean, sample standard deviation, median,
mode, as well as other useful information. To complete this, select Data Analysis again, then
select Descriptive Statistics. In the input range, select the “number of candies in bag” column.
Include the first row containing the label. Make sure the grouped by columns is selected and
check the box next to “Labels in first row”. For the output, select new worksheet ply and name it
Descriptive Stats. Check the box next to “Summary Statistics”.

You can also do this part in StatCrunch. With the “number of candies in bag” data copied in the
previous step, select Stat > Summary Stats > Columns. In the popup window, select the name of
the column that contains your data, then click “Calculate”. The output can be copied and pasted
into your Excel file.

3 pts. Finally, in another worksheet titled “Part 2 Summary”, please summarize the following
information from this part of the project:
     Total number and calculated proportions (sample proportions) for each color
     Sample mean number of candies per bag
     Sample standard deviation of mean number of candies per bag
     Written description of the histogram. Describe its shape: normal, skewed, etc. Also
        identify any potential outliers.
     Sample sizes of this project
            o Total number of candies sampled (total of the number of candies in bag column).
                This is the sample size for all future parts dealing with color proportions.
            o    Total number of bags sampled (number of rows of data). This is the sample size
                for all future parts dealing with the mean and standard deviation number of
                candies per bag.

NOTE: You should be using the combined class data set, not your sample of three bags.

It is imperative that you correctly complete the Part 2 Summary as we will be using the
information summarized on that page for ALL the remaining parts of the project. To help keep
the sample sizes straight, remember that when you calculated the proportion of each color, you
divided by the total number of candies sampled. When you calculated the mean number candies
per bag, you divided by the total number of bags.

At the end of this project, you will be writing a report, explaining the method and presenting the
results from each part of the project. You might find it useful to write this as you complete the
work, so the report will be mostly written by the time it is assigned.


                                            MAT 300
                                         M&Ms® Project
                                          Part 3 (21 pts)
We will be constructing confidence intervals for the proportion of each color as well as the mean
number of candies per bag. You will use the methods of 6.3 for the proportions and 6.1 for the
mean. For the Bonus, you will use the sample size formula on page 338.

You can use StatCrunch to assist with the calculations. A link for StatCrunch can be found
under Tools for Success in Course Home. Here is also a link:
http://statcrunch.pearsoncmg.com/statcrunch/larson_les4e/dataset/index.html. You can also find
additional help on both confidence intervals and StatCrunch in the Online Math Workshop under
Tab: “MAT300 Archived Workshops”. Specifically you will be looking for Confidence
Intervals and Using Technology – CI.

Submit your answers in Excel, Word or pdf format. Upload your file to the dropbox. If
calculating by hand, be sure to keep at least 4-6 decimal places for the sample proportions
to eliminate large rounding errors.

3 pts. Construct a 95% Confidence Interval for the proportion of blue M&Ms® candies.

3 pts. Construct a 95% Confidence Interval for the proportion of orange M&Ms® candies.

3 pts. Construct a 95% Confidence Interval for the proportion of green M&Ms® candies.

3 pts. Construct a 95% Confidence Interval for the proportion of yellow M&Ms® candies.

3 pts. Construct a 95% Confidence Interval for the proportion of red M&Ms® candies.

3 pts. Construct a 95% Confidence Interval for the proportion of brown M&Ms® candies.

3 pts. Construct a 95% Confidence Interval for the mean total number of candies (large
samples).

BONUS: 5 pts. How many candies should be sampled to obtain a 95% CI of the proportion of
blue candies with a 4% margin of error if the known proportion of blue candies is 0.24?

HELP:
Color Proportions
You will need the information from the Part 2 Summary. For the colors, the confidence intervals
need to be found using the formulas in section 6-3 for proportions. The margin of error formula
is




   is the sample proportion of the color. It will change for each color.
   is found by 1 - , so it will also change for each color.
n is the total number of candies sampled.

So let us do an example with “purple”. Let’s say there were 732 purple candies out of 3500 total
candies. The sample proportion of purple candies is 732/3500 = 0.209143. This is what you did
in part 2. Now to find the confidence interval, we need to calculate E. Let's construct a 95% CI.
For that confidence level (95), the z-value is 1.96. We also need
 : =1-        = 1 - 0.209143 = 0.790857.
Now let's plug in:




The confidence interval is found by     - E,   +E
    - E: 0.209143 - 0.013474 = 0.19567 = 19.57%
   + E: 0.209143 + 0.013474 = 0.22262 = 22.26%
So the confidence interval is (0.1957, 0.2226).

You will follow this procedure for EACH color.

IF you have a TI 83/84, you can do the following: STAT, TESTS, 1-PropZInt, ENTER
NOTE: 1-PropZInt: 1 proportion z confidence interval
x = total number of that color
n = total number of candies
Then on the next screen enter 732 next to x, 3500 next to n, 0.95 next to C-Level and then
calculate enter.
On the next screen the second line is the confidence interval: (0.19567,0.22262)
The third line is the value: .2091428571
On the last line is the sample size: 3500

IF you want to use StatCrunch, you will select Stat > Proportions > one sample > with summary.
Then it will ask for the number of successes (total number of that color) and number of
observations (total number of candies). Click on Next. In the next screen, click on the radio
button to the left of “Confidence Interval”, enter the decimal of the confidence level and then
click Calculate. The output will have the confidence interval:
95% confidence interval results:
p : proportion of successes for population
Method: Standard-Wald
Proportion Count Total Sample Prop.            Std. Err.      L. Limit   U. Limit
P               732 3500       0.20914286 0.006874427 0.19566923 0.2226165
Mean
To find the confidence interval for the mean number of candies, you will need (sample mean),
s (sample standard deviation) and n. All of these values were summarized on Part 2 Summary.

Here n is the number of BAGS sampled. The margin of error formula is



IF using the TI 83/84: STAT, TESTS, ZInterval, Enter.
Select Inpt: Stats
s: enter s value to at least 4 decimal places
   : enter value to at least 4 decimal places
n: enter number of bags sampled
C-Level: enter confidence level desired
Calculate, ENTER
On the next screen the second line is the confidence interval
Then and n.

IF using StatCrunch, it is best if you copy the num. candies in bag data into StatCrunch, but you
can use the summary information. The path is Stat > Z Statistics > one sample > with summary
(if using summary information) or with data (if data is entered into the column).
If using summary: You will be prompted for the sample mean, sample standard deviation and
sample size. Click Next. In the next screen, click the button to the left of Confidence Interval
and then enter the confidence level as a decimal and then click Calculate.
If using data: You will first select the column with the data, then click next. The next screen is
the same as with summary.

At the end of this project, you will be writing a report, explaining the method and presenting the
results from each part of the project. You might find it useful to write this as you complete the
work, so the report will be mostly written by the time it is assigned.

                                            MAT 300
                                         M&Ms® Project
                                          Part 4 (21 pts)

Use the M&Ms® data to complete this assignment. You will be using the methods of 7.4 for the
color proportions and 7.2 for the mean number of candies per bag. For the Bonus you will be
using the methods of 7.5.

You can use StatCrunch to assist with the calculations. A link for StatCrunch can be found
under Tools for Success in Course Home. Here is also a link:
http://statcrunch.pearsoncmg.com/statcrunch/larson_les4e/dataset/index.html. You can also find
additional help on both confidence intervals and StatCrunch in the Online Math Workshop under
Tab: “MAT300 Archived Workshops”. Specifically you will be looking for Hypothesis Tests
and Using Technology – Hypothesis Testing.
Submit your answers in Excel, Word or pdf format. Place the file in the dropbox. Be sure to
state clear hypotheses, test statistic values, critical value or p-value, decision (reject/fail to
reject), and conclusion in English. When doing calculations for the color proportions, keep
at least 4-6 decimal places sample proportions, otherwise you will encounter large rounding
errors.

Masterfoods USA states that their color blends were selected by conducting consumer preference
tests, which indicated the assortment of colors that pleased the greatest number of people and
created the most attractive overall effect. On average, they claim the following percentages of
colors for M&Ms® milk chocolate candies: 24% blue, 20% orange, 16% green, 14% yellow,
13% red and 13% brown.

3 pts. Test their claim that the true proportion of blue M&Ms® candies is 0.24 at the 0.05
significance level.

3 pts. Test their claim that the true proportion of orange M&Ms® candies is 0.20 at the 0.05
significance level.

3 pts. Test their claim that the true proportion of green M&Ms® candies is 0.16 at the 0.05
significance level.

3 pts. Test their claim that the true proportion of yellow M&Ms® candies is 0.14 at the 0.05
significance level.

3 pts. Test their claim that the true proportion of red M&Ms® candies is 0.13 at the 0.05
significance level.

3 pts. Test their claim that the true proportion of brown M&Ms® candies is 0.13 at the 0.05
significance level.

3 pts. On average, they claim that a 1.69 oz bag will contain more than 54 candies. Test this
claim (µ > 54) at the 0.01 significance (σ unknown).

BONUS: 5 pts. It is important that the total number of candies per bag does not vary very
much. As a result of this quality control, the desired standard deviation is 1.5. Test the claim (α
= 0.05) that the true standard deviation for number of candies per 1.69 oz bag is no more than 1.5
(σ < 1.5).

HELP:
Color proportions
Revisiting the purple example from before: we had 732 purple candies out of 3500 total candies.
The sample proportion of purple candies is 732/3500 = 0.2091428571.
Now let's say you want to test that the true proportion of purple candies is 21% (0.21).
First define your hypotheses. Claim: p = 0.21
H0: p = 0.21 (null)
H1: p ≠ 0.21 (alternative)
Next we need to calculate the test statistic. For this type of test, it is a z and a two tailed test. You
have been asked to test at alpha = 0.05, so we will reject the null if the test statistic, z, is positive
and greater than 1.96 OR if the test statistic, z, is negative and smaller than -1.96. (NOTE: This
is the same as if the absolute value of the test statistic is greater than 1.96.)




Review:     → sample proportion (0.209143)
p → assumed value in null (0.21)
q → 1 - p (0.79)
n → total number of candies (3500)

Test statistic:




Because the test statistic is between -1.96 and 1.96, we FAIL TO REJECT. We have insufficient
evidence to suggest the true proportion is not 0.21.
You will follow this procedure for EACH color.

IF using the TI 83/84: STAT, TESTS, 1-PropZTest
Po: assumed proportion (0.21)
x: number of successes (732)
n: total number of candies (3500)
In the next line, select the correct alternative hypothesis/test, then Calculate, Enter.
On the next screen, the second line shows the test.
The next line has the test statistic.
The next line has the p-value of the test (if less than significance level, reject null)
The next two lines have      and n.

IF using StatCrunch, you will want Stat > Proportions > One Sample > with summary. In the
first window, you will enter the same information as for part 3: number of the color (number of
successes) and total number of candies (number of observations). Then click Next, and in the
following window, enter the claimed proportion as a decimal in the box next to “null”, select the
inequality that matches the alternative hypothesis and then click Calculate. The output will
include the test statistic (Z-Stat) and the p-value.
Hypothesis test results:
p : proportion of successes for population
H0 : p = 0.21
HA : p ≠ 0.21
Proportion Count Total Sample Prop.               Std. Err.        Z-Stat      P-value
p                732 3500        0.20914286 0.006884766 -0.12449848             0.9009

Mean
When you test for the mean number of candies per bag, you will need          (sample mean), s
(sample standard deviation) and n (total number of bags) as before.

The test statistic is a z, because we have a large sample.
Test statistic:




IF using the TI 83/84: STAT, TESTS, Z-Test
Input: Stats
0: assumed mean value
: sample or known standard deviation
  : sample mean
N: sample size
Then select the correct alternative hypothesis/test, then Calculate, Enter.
On the next screen, the second line shows the test.
The next line has the test statistic.
The next line has the p-value of the test (if less than significance level, reject null)
The next two lines have and n.

IF using StatCrunch, you will use Stat > Z Statistics > one sample as with part 3.


BONUS
This is a test about a standard deviation. You can use StatCrunch, however, StatCrunch deals
with variances, so you would enter 1.5² = 2.25 as the null value. You would use Stat > Variance
> One Sample. Again, it would be best to use the actual data entered into a column, but you can
also use summary values, as long as you carry at least 4 decimal places.

At the end of this project, you will be writing a report, explaining the method and presenting the
results from each part of the project. You might find it useful to write this as you complete the
work, so the report will be mostly written by the time it is assigned.

                                           M&Ms® Project
                                            Part 5 (3 pts)
Using the methods in Section 8.4, test the hypothesis (α = 0.05) that the population proportions
of red and brown are equal (pred = pbrown). You are testing if their proportions are equal to one
another, NOT if they are equal to one another AND equal to 13%. NOTE: These are NOT
independent samples, but we will use this approach anyway to practice the method. This also
means that n1 and n2 will both be the total number of candies in all the bags. The “x” values for
red and brown are the counts of each we found on the Data page. You will need to calculate the


weighted p:


Be sure to state clear hypotheses, test statistic, critical value or p-value, decision (reject/fail to
reject), and conclusion in English. Submit your answer as a Word, Excel, .rtf or .pdf format and
place in the dropbox.

HELP
You can use StatCrunch or the TI to help with this test. Needed information for both tools
include:
       x1 = number of red
       n1 = total number of candies
       x2 = number of brown
       n2 = total number of candies

For the TI, you will want 2-PropZTest. Then select the appropriate alternative (not equal), and
Calculate then enter. The output will have the test statistic (z), p-value (p), sample p values,
weighted p (   ), then repeat of sample sizes.

For StatCrunch, you will select Stat > Proportions > Two Sample > with summary. The output
will contain the test statistic (Z-Stat) and p-value.

Additional help is available in the Online Math Workshop under MAT300 Archived Workshop.
Specifically Two Sample Inferences and Using Technology – Two Sample.

At the end of this project, you will be writing a report, explaining the method and presenting the
results from each part of the project. You might find it useful to write this as you complete the
work, so the report will be mostly written by the time it is assigned.



                                      M&Ms® Project Report
                                           (15 pts)

A template report file can be found in the course shell: mnmprojectreport.doc. Before your write
your report, watch the video titled “mnmunwrapped.wmv” located in the course shell. It is a
3:30-minute video segment from the TV show “Unwrapped,” showing many parts of the
production process, which might give you some ideas. Ignore the color percentages quoted in the
segment.

       Imagine you are a quality control manager at the Masterfoods plant. Write a two to three
       (2–3) page report on all the parts of the project. Structure your paper using the following
       headers:
          o Introduction: Purpose of Report
          o Project Part 1: Sampling Method
          o Project Part 2: Method, Analysis, Results
          o Project Part 3: Method, Analysis, Results
          o Project Part 4: Method, Analysis, Results
          o Project Part 5: Method, Analysis, Results
          o Quality Control: Assume that at least one of the tests from Part 4 was rejected
              (proportion not equal to targeted amount set by Masterfoods). Discuss how you
              would investigate the operations of the plant to determine why the proportions
              were off the targeted values. Speculate on three or more possible conditions in
              plant and bagging process that could have caused the observed results.
          o Conclusion

       You should explain what was done as well as the results. Tables can be used to present
       results and information. Your audience is a supervisor or manager who is unfamiliar with
       this project and may or may not be familiar with statistical terms. As a result, you will
       either need to explain/define statistical terms or write them in a way that a layman can
       understand.

 You will be graded on the following criteria:
  1. Present the methods, analysis, and results for the five parts of the project. See above
      Project Parts 1 through 5.
  2. Explain how to investigate unexpected results (failed test(s) in Part 4) and speculate on at
      least three plausible causes for the observed results.
  3. Clarity in explaining all statistical terminology in every-day language.
  4. Writing, grammar, sentence structure, APA format.

       The format of the report is to be as follows:
          o Typed, double-spaced, Times New Roman font (size 12), one-inch margins on all
              sides, APA format.
          o Type the question followed by your answer to the question.
          o In addition to the two to three (2–3) pages required, a title page is to be included.
              The title page is to contain the title of the assignment, your name, the instructor’s
              name, the course title, and the date.

 NOTE: You will be graded on the presentation of information, the accuracy and completeness
 of your answers, the logic/organization of the report, the clarity of your explanations, and your
 writing skills (grammar, style, spelling, etc.)

The assignment will be graded using the following rubric and is worth 6% of course grade:
                              Discuss application of course content in the context of a professional setting.
Outcomes Assessed
                              Use technology and information resources to research issues in statistics.
                                    Grading Rubric for M&M® Project Report

                                      0                    10                      20                      30
       Criteria               Unacceptable            Developing              Competent               Exemplary
1. Present the            Did not submit or      Partially presented     Sufficiently            Fully presented the
   methods, analysis,     did not present the    the methods,            presented the           methods, analysis,
   and results for the    methods, analysis,     analysis, and results   methods, analysis,      and results for the
   five parts of the      and results for the    for the five parts of   and results for the     five parts of the
   project.               five parts of the      the project;            five parts of the       project; completed
                          project; or omitted    completed               project; completed      with 90-100%
                          key information        with 60-79%             with 80-89%             accuracy and
                          and/or included        accuracy and            accuracy and            thoroughness.
                          irrelevant             thoroughness.           thoroughness.
                          information.
                          Completed with less
                          than 60% accuracy,
                          thoroughness, and
                          logic.
2. Explain how to         Did not complete       Partially explained     Sufficiently            Fully explained how
   investigate            the assignment or      how to investigate      explained how to        to investigate
   unexpected results     failed to explain      unexpected results      investigate results     unexpected results
   (failed test(s) in     how to investigate     and speculated on at    and speculated on at    and speculated on at
   Part 4) and            unexpected results     least one plausible     least two plausible     least two plausible
   speculate on at        or to speculate on     cause; completed        causes; completed       causes; completed
   least three            plausible causes; or   with 60-79%             with 80-89%             with 90-100%
   plausible causes       omitted key            accuracy and            accuracy and            accuracy and
   for the observed       information and/or     thoroughness.           thoroughness.           thoroughness.
   results.               included irrelevant
                          information.
                          Completed with less
                          than 60% accuracy,
                          thoroughness, and
                          logic.
3. Clarity: Explain       Did not complete       Explained partially     Explained               Explained fully all
  all statistical         the assignment or      all statistical         sufficiently all        statistical
  terminology in          did not explain all    terminology in          statistical             terminology in
  every-day               statistical            every-day language      terminology in          every-day language;
  language.               terminology in         or explained            every-day language;     completed with 90-
                          every-day language.    sufficiently some of    completed with 80-      100% accuracy and
                          ; or omitted key       the statistical         89% accuracy and        thoroughness.
                          information and/or     terminology in          thoroughness.
                          included irrelevant    every-day language;
                          information.            completed with 60-
                          Completed with less    79% accuracy and
                          than 60% accuracy,     thoroughness.
                          thoroughness, and
                          logic.
4. Writing –              Did not complete       Had 6 - 7 different     Had 4 - 5 different     Had 0 - 3 different
   Grammar,               the assignment or      errors in grammar,      errors in grammar,      errors in grammar,
   sentence structure,    had 8 or more          sentence structure,     sentence structure,     sentence structure,
   paragraph              different errors in    paragraph structure,    paragraph structure,    paragraph structure,
   structure, spelling,   grammar, sentence      spelling,               spelling,               spelling,
                              0                    10                 20                  30
   Criteria           Unacceptable            Developing         Competent           Exemplary
punctuation, APA   structure, paragraph   punctuation, or    punctuation, or     punctuation, or
usage.             structure, spelling,   APA usage. (Many   APA usage. (Minor   APA usage.
                   punctuation, or        issues)            issues)
                   APA usage. (Major
                   issues)

								
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