MA 214  Probability and Statistics for Business

Dr. Ed Donley

 

Hypothesis Test Review

 

1.   An American Demographics study in 1980 found that 40% of new car buyers were women.  Suppose that in a random sample of 120 new car buyers in 1992, 57 were women.  Try to show that a higher proportion of car buyers in 1992 are women.  Use a = 0.05.

 

2.   A quality control inspector for the Bouncy Rubber Band Company wants to show that the average weight of their 6 ounce boxes is actually greater than 6 ounces.  If a sample of 81 boxes had a mean weight of 6.02 ounces and a standard deviation of 0.09, find the p-value of the hypothesis test.

 

3.   A sample of 25 managers for a regional accounting firm had a mean salary equal to $38,000 with a standard deviation of $10,000.  A partner for the firm told new recruits that the average salary for managers is $42,000 or more.  Should we challenge her claim?  Use a = 0.05.

 

4.   In order to determine if more than half of all customers' favor a new package design, both the old and new designs are left on the store's shelves.  After 50 purchases have been made, 20 are of the old design and 30 are of the new design.  What should we conclude at the 5% significance level?

 

5.   A company's retail sales records show that the average monthly expenditure per person last year was $10.  We wish to see if there is a significant change for this year.  Test this with a = 0.05.  A random sample of 120 customers had an average expenditure of $9.40 with a standard deviation of $0.45.

 

6.   A shipping company wants to see if a new barnacle-resistant paint is more effective than their current brand.  On each of five ships, a patch section of the hull is painted with the current brand and another patch is painted with the new brand.  The number of barnacles per square foot are listed below.  Perform the hypothesis test with  a = 0.05.

 

                                                                                                             ship

 

1

2

3

4

5

current brand

12

10

6

18

10

new brand

10

10

5

15

11

 

7.      In the past, patrons of a cinema have spent an average of $2.50 for popcorn and other snacks.  A recent sample of 50 patrons spent an average of $2.10 with standard deviation $0.90.  Can we conclude, at the 0.05 significance level, that expenditures have declined?

 

8.      In 1986, the United Dairy Industry Association reported that 135 out of 276 persons in the 17-19 age group seldom eat cottage cheese.  At the 0.05 significance level, can we conclude that more than 45% of all persons in this age group seldom each cottage cheese?

 

9.      For a special pre-New Year's Eve show, a radio station personality has invited five local citizens to help demonstrate to listeners the adverse effect of alcohol on reaction time.  Given the reaction times below, in seconds, has the program host demonstrated his point?  Let a = 0.05.

 

                                                                                                                        Subject

 

1

2

3

4

5

Before Drinking

0.32

0.39

0.36

0.41

0.37

After Drinking

0.39

0.44

0.49

0.53

0.46

 

 

10.    According to the U.S. Bureau of Labor Statistics, personal expenditures for entertainment averaged $349 per person in the Northeast and $420 in the West.  Assume these data were based on sample sizes of 800 and 600 and standard deviations of $215 and $325, respectively.  Test for a difference in the average expenditures of the two regions, with a = 0.05.

 

11.    Suppose the building specifications in a certain city require that sewer pipe have a mean breaking strength of more than 2500 pounds per linear foot.  A contractor, wishing to use a certain manufacturer's pipe, selected a random sample of 7 pipe sections and found that they had a mean strength of 2571 and standard deviation 115.  Can the contractor use this manufacturer's pipe?  Let a = 0.10.

 

12.    The average time required for a novice to assemble an electronic kit at a manufacturing plant is 3 hours.  A new instructional booklet is written that is intended to reduce the assembly time required by novices.  Using this booklet, 15 novices required a mean of 2.90 hours with a standard deviation of 0.20 hours to complete the assembly.  Should we conclude, at the 0.05 significance level, that the new booklet is effective?

 

13.    A sample of 20 investors serviced by one account manager has an average of $23,000 in transactions with a standard deviation of $8000.  A sample of 25 investors serviced by another account manager has an average of $28,000 with a standard deviation of $9000.  Test for a difference in the transaction averages for customers serviced by the two account managers.  Let a = 0.05.