# Central Limit Theorem Excel Worksheet by crf13445

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```									  • SPSS does not calculate confidence intervals for proportions.
• The Excel spreadsheet that I used to calculate the proportions

12/15/2010                                                    Slide 1
The introductory statement in the question indicates:
• The data set to use: GSS2000R.SAV
• The task to accomplish: a confidence interval for proportions
• The variable to use in the analysis: self-employment [wrkslf].
• The category to use for the confidence interval: self-employed

12/15/2010                                                                      Slide 2
The first statement asks about the level of
measurement. To compute a confidence interval
for proportions, the variable must be categorical.

We will use a frequency distribution to get a list of
the values for the variable.

12/15/2010                                                           Slide 3
To compute the frequency distribution,
select the Descriptive Statistics > Frequencies
command from the Analyze menu.`

12/15/2010                                                     Slide 4
First, we move the
variable wrkslf to the
Variable(s) list box.

Second, click on the
OK button to
produce the output.

12/15/2010                                                   Slide 5
The variable includes
two categories,
justifying its use as a
categorical variable.

12/15/2010                             Slide 6
Since the variable self-employment [wrkslf]
can be used as a categorical variable, we
mark the statement as correct.

12/15/2010                                                 Slide 7
sample size requirements. We can use the
frequency distribution to get the number
and percentage of cases in each category.

12/15/2010                                               Slide 8
The sample size is large enough to make the sampling
model for the sample proportions approximately normal
based on the Central Limit Theorem if there are 10 or more
cases in both the target category for the confidence interval
and the other category in the distribution of the variable.

There were 32 in the category "self-
employed". With 250 valid cases in
the distribution, the number of cases
in the other category was 218.

Both groups used to compute the
confidence interval had the required
minimum of 10 cases. The sample
size requirement is satisfied.

12/15/2010                                                                      Slide 9
Both groups used to compute the
confidence interval had the required
minimum of 10 cases. The sample size
requirement is satisfied.

Mark the check box for a correct answer.

12/15/2010                                              Slide 10
the 95% confidence interval.

SPSS does not compute the
confidence interval for a
proportion. We will use Excel to
calculate the confidence interval.

12/15/2010                                                                   Slide 11
To compute the confidence interval in Excel, we need two
items of information from the SPSS frequency table:
• The valid percent in the target category
• The total number of valid cases

12/15/2010                                                              Slide 12
When you open the Excel workbook
ConfidenceIntervalForProportions.xls,
you will see the following.
Directions for using the
worksheet are shown in
rows 1 and 2.

Unless you unprotect the
worksheet, the only cells
you can enter data in are
B4 and B6.

The worksheet includes the
formulas for all three of the
confidence intervals of interest:
90%, 95%, and 99%.

12/15/2010                                                                                     Slide 13
This view shows the
formulas that were
entered in each of the
orange cells that
calculate the results.

You should not have
to change them.

12/15/2010                            Slide 14
When cells B4 and B6 are
empty, this is what the
worksheet will look like.

12/15/2010                               Slide 15
Next, we enter data from
the frequency table to
compute the interval.

The proportion of survey
respondents who were
self-employed was 0.128.

The proportion of survey
respondents in the categories
other than self-employed
was 0.872 (1.00 - 0.128).

12/15/2010                                                                    Slide 16
I entered the number of
valid cases from the SPSS
frequency table.

To compute the standard error based on
the sample proportion, we multiply the
proportion in the category (0.1280)
times the proportion in other categories
(0.8720), divide by the number of valid
cases (250), and compute the square
root of the result [square root(0.1208 x
0.8702 ÷ 250) = 0.0211].

12/15/2010                                          Slide 17
For a 95% confidence interval, we
compute the margin of error by
multiplying the standard error by
1.96 (1.96 x 0.0211 = 0.0414).

12/15/2010                                       Slide 18
The lower bound of the 95%
confidence interval is computed by
subtracting the margin of error from
the proportion in the target category
(0.1280 - 0.0414 = 0.0866). The upper
bound of the 95% confidence interval
is computed by adding the margin of
error to the proportion in the target
category (0.1280 + 0.0414 = 0.1694).

12/15/2010                                       Slide 19
The lower bound of the 95% confidence
interval is 0.0866 (or 8.7%). The upper
bound of the 95% confidence interval is
0.1694 (or 16.9%).

The statement that "we can be 95%
confident that between 8.7% and 16.9%
of all survey respondents were self-
employed" is correct.

Mark the check box for a correct answer.

12/15/2010                                                    Slide 20
If we violate the level of measurement or
sample size requirement, it not appropriate
to compute the confidence interval. In this
case, we would mark “None of the above.”

12/15/2010                                                 Slide 21
Variable can be               Do not mark
No       check box.
treated as categorical?

Problem will state target                                  Mark only “None of
category. All other                                           the above.”
categories are combined               Yes
into “other” category.                                           Stop.
Mark statement
check box.

10+ subjects in target            Do not mark
No        check box.
and other categories?

Mark only “None of
the above.”
Yes
Stop.
Mark statement
check box.

12/15/2010                                                                       Slide 22
Confidence interval        Do not mark
No    check box.
stated correctly?

Stop.
Yes

We do not mark “None
Mark statement                          of the above” because
check box.                            level of measurement
and sample size should
be marked if we got to
this step.

12/15/2010                                                            Slide 23

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