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# Hypothesis Testing Problems

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Chapter 10
1. Rutter Nursery Company packages its pine bark mulch in 50-pounds bags. From a long history, the production department reports that the distribution of the bag weights follows the normal distribution and the standard deviation of this process is 3 pounds per bag. At the end of each day, Jeff Rutter, the production manager, weighs 10 bags and computes the mean weight of the sample. Below are the weights of 10 bags from todays' production.

45.6 47.7 47.6 46.3 46.2 47.4 49.2 55.8 47.5 48.5

a. Can Mr. Rutter conclude that the mean weight of the bags is less than 50 pounds? Use the 0.01 significance level. (show all work)
b. In a brief report, tell why Mr. Rutter can use the Z distribution as the test statistic.
c. Compute the p-value (SHOW ALL WORK)

2. According to a recent survey, Americans get a mean of 7 hour of sleep per night. A random sample of 50 students at West Virginia University revealed the mean number of hours slept last night was 6 hours and 48 minutes (6.8 hours). The standard deviation of the sample was 0.9 hours. Is it reasonable conclude that students at West Virginia sleep less than the typical American? Compute the p-value. (show all work).

3. In recent years the interest rate on home mortgages has declined to less than 6.0 percent. However, according to a study by the federal Reserve Board the rate charges on credit card debt is more than 14 percent. Listed below is the interest rate charged on a sample of 10 credit cards.

14.6 16.7 17.4 17.8 15.4 13.1 15.8 14.3 14.5

Is it reasonable to conclude the mean rate charges is greater than 14 percent? Use the 0.01 significance level. (show all work)

Chapter 12
22. A large company is organized into three functional areas: manufacturing, marketing, and research and development. The employees claim that the company pays women less than men for similar jobs. The company randomly selected four males and four females in each area and recorded their weekly salaries in dollars

Area/Gender Female Male
Manufacturing 1016, 1007, 875, 968 978, 1056, 982, 748
Marketing 1045, 895, 848, 904 1154, 1091, 878, 876
Research and Development 770, 733, 844, 771 926, 1055, 1066, 1088

A. Draw the interaction graph. Based on your observations, is there an interaction effect. Based on the graph, describe the interaction effect of gender and area on salary.
B. Use the 0.05 level for gender, area, and interaction effects on salry. Report the statistical results
C. Compare the male and female mean sales for each area using statistical techniques. What do you recommend to the distributor?

29. A Consumer organization wants to know whether there is a difference in the price of a particular toy at three different types of stores. The price of the toy was checked in a sample of five discount stores, five variety stores, and five department stores. The results are shown below. Use the 0.05 significance level. (SHOW ALL WORK)

Discount Variety Department
\$12 \$15 \$19
13 17 17
14 14 16
12 18 20
15 17 19

Chapter 11

1. The federal government recently granted funds for a special program designed to reduce crime n high-crime areas. A study of the results of the program in eight high-crime areas of Miami, Florida, yielded the following results.

Numbers of Crimes by Area
A B C D E F G H
Before 14 7 4 5 17 12 8 9
After 2 7 3 6 8 13 3 5

Has there been a decrease in the number of crimes since the inauguration of the program? Use the 0.01 significance level. Estimate the p-value. (show all work)

2. The Engineering Department at Sims Software, Inc., recently developed two chemical solutions designed to increase the usable life of computer disks. A sample of disks treated with the first solution lasted 86,78,66,83,84,81,109,65, and 102 hours. Those treated with the second solution lasted 91, 71, 75, 76, 87, 79, 73, 76, 79, same. At the 0.10 significance level, can we conclude that there is a difference in the length of time the two types of treatment lasted?

3. Lester Hollar is vice president for human resources of a large manufacturing company. In recent years he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each absent in the six months before the exercise program began and in the last six months. Below are the results. At the 0.05 significance level, can he conclude that the number of absences has declined? Estimate the p-value.

Employee Before After
1 6 5
2 6 2
3 7 1
4 7 3
5 4 3
6 3 6
7 5 3
8 6 7

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#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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## One and Two Tailed Tests: Hypothesis Testing Problem

Ho: u = 50
H1: u not = 50
The sample mean is 49, and the sample size is 36. the population standard deviation is 5. Use the .05 significance level.

a. Is this a one or two tailed test.
b. What is the decision rule?
c. What is the value of the test statistic?
d. What is your decision regarding Ho?
e. What is the p-value? Interpret it.

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