# Hypothesis Testing: Mean & Variance

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One- and Two-Sample Tests of Hypothesis, Variance, and Chi-squared Analysis Problem Sets

? Resource: Statistical Techniques in Business & Economics

? Prepare responses to the following exercises from the text.

o Exercises 31, 32, and 38 (Ch. 10)

o Exercises 27, 46, and 52 (Ch. 11)

o Exercises 23 and 28 (Ch. 12)

o Exercises 19 and 20 (Ch. 17)

Chapter 10

31. A new weight-watching company, Weight Reducers International, advertises that those who join will lose, on the average, 10 pounds the first two weeks with a standard deviation of 2.8 pounds. A random sample of 50 people who joined the new weight reduction program revealed the mean loss to be 9 pounds. At the .05 level of significance, can we conclude that those joining Weight Reducers on average will lose less than 10 pounds? Determine the p-value.

32. Dole Pineapple, Inc., is concerned that the 16-ounce can of sliced pineapple is being overfilled. Assume the standard deviation of the process is .03 ounces. The quality control department took a random sample of 50 cans and found that the arithmetic mean weight was 16.05 ounces. At the 5 percent level of significance, can we conclude that the mean weight is greater than 16 ounces? Determine the p-value.

38. A recent article in the Wall Street Journal reported that the 30-year mortgage rate is now less than 6 percent. A sample of eight small banks in the Midwest revealed the following 30- year rates (in percent):

4.8 5.3 6.5 4.8 6.1 5.8 6.2 5.6

At the .01 significance level, can we conclude that the 30-year mortgage rate for small banks is less than 6 percent? Estimate the p-value.

Chapter 11

27. A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. The information is summarized below.

Statistic Men Women

Sample mean 24.51 22.69

Population standard deviation 4.48 3.86

Sample size 35 40

At the .01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? What is the p-value?

46. Grand Strand Family Medical centre is specifically set up to treat minor medical emergencies for visitors to the Myrtle Beach area. There are two facilities, on in the Little River area, and the other in Murrells Inlet. The Quality Assurance Department wishes to compare mean waiting times for patients in two locations. Samples of waiting times, reported in minutes follow:

Location Waiting time

Little River 31.73 28.77 29.53 22.08 29.47 18.60 32.94 25.18 29.82 26.49

Murrells Inlet 22.93 23.92 26.92 27.20 26.44 25.62 30.61 29.44 23.09 23.10 29.69 22.31

Assume the population standard deviations are not the same. At the .05 significance level, is there a difference in the mean waiting time?

52. The president of the American Insurance Institute wants to compare the yearly costs of auto insurance offered by two leading companies. He selects a sample of 15 families, some with only a single insured driver, others with several teenage drivers, and pays each family a stipend to contact the two companies and ask for a price quote. To make the data comparable, certain features, such as the deductible amount and limits of liability, are standardized. The sample information is reported below. At the .10 significance level, can we conclude that there is a difference in the amounts quoted?

Family Car Insurance Mutual Insurance

Becker $2,090 $1,610

Berry 1,683 1,247

Cobb 1,402 2,327

Debuck 1,830 1,367

DuBrul 930 1,461

Eckroate 697 1,789

German 1,741 1,621

Glasson 1,129 1,914

King 1,018 1,956

Kucic 1,881 1,772

Meredith 1,571 1,375

Obeid 874 1,527

Price 1,579 1,767

Phillips 1,577 1,636

Tresize 860 1,188

Chapter 12

23. A real estate agent in the coastal area of Georgia wants to compare the variation in the selling price of homes on the oceanfront with those one to three blocks from the ocean. A sample of 21 oceanfront homes sold within the last year revealed the standard deviation of the selling prices was $45,600. A sample of 18 homes, also sold within the last year, that were one to three blocks from the ocean revealed that the standard deviation was $21,330. At the .01 significance level, can we conclude that there is more variation in the selling prices of the oceanfront homes?

28. The following is a partial ANOVA table.

Source Sum of Squares df Mean square F

Treatment 2

Error 20

Total 500 11

Complete the table and answer the following questions. Use the .05 significance level.

a. How many treatments are there?

b. What is the total sample size?

c. What is the critical value of F?

d. Write out the null and alternate hypotheses.

e. What is your conclusion regarding the null hypothesis?

Chapter 17

19. In a particular market there are three commercial television stations, each with its own evening news program from 6:00 to 6:30 P.M. According to a report in this morning's local newspaper, a random sample of 150 viewers last night revealed 53 watched the news on WNAE (channel 5), 64 watched on WRRN (channel 11), and 33 on WSPD (channel 13). At the .05 significance level, is there a difference in the proportion of viewers watching the three channels?

20. There are four entrances to the Government Centre Building in downtown Philadelphia. The building maintenance supervisor would like to know if the entrances are equally utilized. To investigate, 400 people were observed entering the building. The number using each entrance is reported below. At the .01 significance level, is there a difference in the use of the four entrances?

Entrance Frequency

Main street 140

Broad street 120

Cherry street 90

Walnut street 50

Total 400

#### 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.