Statistic assignment

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					1. Which of the following is an example of graphs used to describe data?

A) Histograms

B) Bar charts

C) Both A and B are correct.

D) None of the above



2. Recently, a major tire manufacturer stated in its advertising that its tires with a new tire tread design
will last more than 50,000 miles on average. A consumer agency collected a subset of these tires and
tested them in very controlled conditions. Based on this test, the agency concluded that the
manufacturer was justified in making this claim. The process described is an example of:

A) descriptive statistics.

B) hypothesis testing.

C) statistical inference.

D) Both B and C are correct.



3. If a stratified random sample is to be conducted, which of the following is true?

A) The population will be broken down into subgroups called strata.

B) Each subgroup should contain items that are homogeneous with respect to the characteristic of
interest.

C) If effective, the total required sample size should be less than that which would be needed if a simple
random sample were selected.

D) All of the above.



4. A small company has 7 employees. The numbers of years these employees have worked for this
company are shown as follows:

4       14       3           16   9       8       16

Based upon this information, what is the mode number of years that employees have been with this
company
5. Consider the following data, which represent the number of miles that employees commute from
home to work each day. There are two samples: one for males and one for females.

Males:

13       5        2       23     14      5

Females:

15       6        3       2      4       6

Which of the following statements is true?

A) The female distribution is more variable since the range for the females is greater than for the males.

B) Females in the sample commute farther on average than do males.

C) The males in the sample commute farther on average than the females.

D) Males and females on average commute the same distance.



6. What is meant by the concept, standardizing the data? Explain why a decision maker may wish to
compute a standardized value. What is the standardized value and what is the formula to derive the
value?

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7. The Cromwell Construction Company has the opportunity to enter into a contract to build a mountain
road. The following table shows the probability distribution for the profit that could occur if it takes the
contract:

         Profit   Probability

         $30,000          0.15

         $50,000          0.20

         $70,000          0.30

         $100,000         0.35

What is the probability of profit ?
8. The actual mean fill volume for all bottles of a soft drink product that were filled on a Tuesday is
11.998 ounces. A sample of 64 bottles was randomly selected and the sample mean fill volume was
12.004 ounces. Find the sampling error (please show your work).




9. ) The makers of a particular type of candy have stated that 75 percent of their sacks of candy will
contain 6 ounces or more of candy. A consumer group that studies such claims recently selected a
random sample of 100 sacks of this candy. Of these, 70 sacks actually contained 6 ounces or more. The
probability that 70 or fewer sacks would contain 6 ounces or less is approximately 0.1251.

True _____       False _____



10. A statement in the newspaper attributed to the leader of a local union stated that the average
hourly wage for union members in the region is $13.35. He indicated that this number came from a
survey of union members. If an estimate was developed with 95 percent confidence, we can safely
conclude that this value is within 95 percent of the true population mean hourly wage.

Do you agree or disagree and why?



11. When someone is on trial for suspicion of committing a crime, the hypotheses are:

        H O : innocent

        H A : guilty

What type of error can be correct?



12. The t-distribution can be used to test hypotheses about the difference between two population
means given the following two assumptions:

        - each population is normally distributed, and

        - the two populations have equal variances.

True _____               False _____
13. . A machine that is used to fill soda pop cans with pop has an adjustable mean fill setting, but the
standard deviation is not supposed to exceed 0.18 ounces. To make sure that this is the case, the
managers at the beverage company each day select a random sample of n = 6 cans and measure the fill
volume carefully. In one such case, the following data (ounces per can) were observed. What is the test
statistic (use Chi Square). Run the test. Show your work please.

12.29      11.88         12.03    12.22   11.76    11.98




14. The U.S. Golf Association provides a number of services for its members. One of these is the
evaluation of golf equipment to make sure that the equipment satisfies the rules of golf. For example,
they regularly test the golf balls made by the various companies that sell balls in the United States.
Recently, they undertook a study of two brands of golf balls with the objective to see whether there is a
difference in the mean distance that the two golf ball brands will fly off the tee. To conduct the test, the
U.S.G.A. uses a robot named "Iron Byron," which swings the club at the same speed and with the same
swing pattern each time it is used. The following data reflect sample data for a random sample of balls
of each brand.

Brand A:           234      236     230   227     234      233     228     229     230      238

Brand B:           240      236     241   236     239      243     230     239     243      240

Given this information, what is the test statistic for testing whether the two population variances are
equal?



15. Recently, a company tested three different machine types to see if there was a difference in the
mean thickness of products produced by the three. A random sample of ten products was selected from
the output from each machine. Given this information, what is the proper ANOVA design to test
whether the means are equal?

__________________________________________________________________________




16. . The State Transportation Department is thinking of changing its speed limit signs. It is considering
two new options in addition to the existing sign design. At question is whether the three sign designs
will produce the same mean speed. To test this, the department has conducted a limited test in which a
stretch of roadway was selected. With the original signs up, a random sample of 30 cars was selected
and the speeds were measured. Then, on different days, the two new designs were installed, 30 cars
each day were sampled, and their speeds were recorded. Suppose that the following summary statistics
were computed based on the data:



        x 1 = 62.1       x 2 = 58.94      x 3 = 71.2

        SST = 6016



Based on these sample results and a significance level equal to 0.05, assuming that the null hypothesis
of equal means has been rejected, the Tukey-Kramer critical range is:




17. Name the various types of ANOVA TESTS that are available to you to run on a business problem or
management dilemma situation. Explain the detail of each type of ANOVA.

_____________________________________________________________________________________



18. A dependent variable is the variable that we wish to predict or explain in a regression model.

True _____               False _____



19. Explain the difference between regression and multiple regression.

_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
____________________________________________________________________________________

20. If two variables are related in a positive linear manner, the scatter plot will show points on the x,y
space that are generally moving from the lower left to the upper right.

True _____               False _____



21. Explain the difference between correlation and regression as statistical tests.
_____________________________________________________________________________________
_____________________________________________________________________________________
____________________________________________________________________________________

22. The multiple coefficient of determination measures the percentage of variation in the dependent
variable that is explained by the independent variables in the model. Why is the R 2 value important in a
multiple regression model with several independent variables?

_____________________________________________________________________________________
_____________________________________________________________________________________
____________________________________________________________________________________.

23. Match column A with column B

_____ Correlation                                 A. Chi Square

____    Regression                                B. two variables are related, linearly (not cause and

                                                          effect)

_____ Multiple regression                         C. statistical technique in which a dependent variable
                                                  (y) is predicted by 2 or more independent variables (X)

_____ non-parametric test                         D. Linear relationship between X and Y – a tool used for

                                                  prediction and investigating for cause and effect

24. The table at the right gives the miles per gallon and the load capacity for 6 SUV’s.

a.      Develop a scatter diagram for the data. Remember X and Y
          axes. (Answer a. and b.)                                         Miles per
                                                                           Gallons         Load Capacity

                                                                           19              860

                                                                           17              970

                                                                           16              1035

                                                                           16              1165

                                                                           14              1180

                                                                           13              1360

				
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