# Questions below link to book below

#### Chapter Formulas

 Formula 11.1 C.I..95=±t(SEM)+M The formula for the confidence interval of the population mean. Formula 11.2 C.I..95=±t(SEd)+(M1−M2) The formula for the confidence interval of the difference. Formula 11.3 C.I..68=±1(SEest)+y′ The formula for the .68 confidence interval of the prediction. Formula 11.4 C.I.=±tn−2(SEest)+y′ The formula for the confidence interval of the prediction.

#### Management Application Exercises

Unless otherwise stated, use p = .05 in all your answers.

1.       A hardware retailer has averaged sales of \$64,235, with a standard deviation of \$5,918, for a 12-month period. The mean monthly sales for all retailers in the chain are \$59,844. Are this hardware retailer’s sales significantly different from those of all retailers in the chain at p = .05? Are they significantly different at p = .01?

2.       Calculate a .95 confidence interval for the data in problem 1. Explain your findings in lay terms. What question does the confidence interval answer?

3.       Calculate C.I..99 for the data in problem 1. What is the effect of changing the confidence level on the width of the interval? Why?

4.       There are two groups of eight sales representatives for a pharmaceutical company in two regions of the country. For group 1, the average monthly charges to expense accounts are \$387, with s = \$22.73. For group 2, the average is \$344, with s = 18.19. Is the difference between the two groups statistically significant at p = .05? Are they significantly different at p = .01?

5.       Calculate a C.I..95 for the difference for the item 4 data. Which value(s) represent the point estimate of the difference, and which value(s) indicate(s) the interval estimate of the difference for the item 4 data?

6.       What could be done to narrow the interval estimate for the item 4 data?

7.       A car dealer is using the number of years customers have owned their vehicles to predict how long it will be before they elect to replace them. The correlation between the two is rxy = −.723 (the longer they have owned their present vehicles, the more quickly they are expected to replace them). The other relevant data are as follows for 32 customers:

 Mean Standard Deviation Years owned present vehicle 4.551 1.627 Time until expected replacement 2.259 1.338

9.       How long will it be until a customer who has owned the vehicle 6.5 years is likely to replace it?

10.   Calculate .95 and .99 confidence intervals for the prediction in item 7.

11.   How will a larger standard deviation in the criterion variable affect the width of the confidence intervals in item 8? Why?

12.   What does a .95 confidence interval of the prediction for the item 7 data reveal?

1. Phi coefficient measures the strength of the relationship between two nominal variables when at least one of them has only two categories.

Chapter Formulas

 Formula 12.1 Χ2=Σ(fo−fe)2fe is the formula for the chi-square test statistic. The same formula is used for both “goodness of fit” test and for the r × k chi-square test of independence.

 Formula 12.2 ϕ=(X2/n) Phi coefficient is the measure of the correlation for two nominal variables when the chi-square test of independence indicates a significant result, and when one of the variables involved has two or fewer categories.

 Formula 12.3 Vϕ2/(smaller of rows or columns)−1 When the test of independence is significant and both variables have at least three categories, Cramer’s V is calculated rather than phi coefficient. V requires phi, however, which must be calculated first.

Management Application Exercises

Unless otherwise stated, use p = .05 in all your answers.

1. Three new movies, each with the potential to be a blockbuster, are released on the same day. Reporters from the local television station are interested to see whether one appears to have caught the public attention more than the others. The reporter goes to the local multiplex and asks those waiting to buy tickets which movie they intend to see. On the basis of results from 52 people, are there significant differences in movie preferences? The data are as follows:

Fantasy Haven: 22

Night of Terror: 18

Fists of Glory: 12

1. Data from behavioral psychology indicate that administering a tangible reward to subjects will prompt response levels twice as frequent as from subjects who receive a nontangible reward. To test this notion in a business context, two sales seminars are compared. In one seminar, sales representatives are tossed a piece of candy every time they ask a relevant question or provide an insightful comment. In the other seminar, only verbal reinforcement is provided. At the end of the seminars, data are as follows:

verbal reinforcement seminar—17 questions/comments

tangible reward seminar—27 questions/comments

1. What is the fe value for each group?
2. Are the results consistent with the expectation?
1. A Department of Labor study of education and employment found that unemployed full-time students take twice as many units as students who are full-time employees and 1.5 times more units than students who are part-time employees.
1. If the fe for the unemployed student is 16 units, what are the fe values for students who work part time and full time?
2. If the student who is unemployed takes 16 units, the student who is employed part time takes 14 units, and the full-time employee takes 12 units, is the expectation supported?
2. In a management trainee program for a multinational corporation, trainees are expected to learn a foreign language. Besides classes at a language training institute, tutors are available. Experience suggests that those learning Japanese seek the help of tutors twice as frequently as those who are learning Spanish. Among 20 students of Japanese, 16 ask for the help of tutors. Among 30 students of Spanish, 8 ask for tutors’ help.
1. What are the fe values?
2. Are results consistent with prior experience?
3. In this instance, what does HA specify?
3. A marketing analyst is examining the relationship between shoppers’ ethnicity and the purchase of certain grocery item. From ethnic group A, 2 of 12 people purchased the item. From ethnic group B, 5 of 10 people purchased the item. From ethnic group C, 4 of 14 people purchased the item.
1. Are the shoppers’ ethnicities and the tendency to purchase this item independent?
2. If not, what is the correlation?
4. During the summer months, when electricity usage is high, the power company appeals to customers to reduce consumption by 10% as a public service to avoid blackouts. An alternative is to offer rebates to customers who reduce usage by 10% compared to the same month the previous year. Among 50 randomly selected customers just asked to reduce electricity use, 14 reduce their use by 10% or more. Among 50 randomly selected customers offered rebates, 25 reduce their electricity use by 10%. Are the differences between the public service appeal and the rebates statistically significant?
5. A number of nonprofit groups use fireworks sales as the major fundraiser in the days before the 4th of July. Some of the nonprofits are service groups such as the Veterans of Foreign Wars. Others are intended for support of groups like the cheerleaders from the local high school. The questions are whether those two groups attract different numbers of customers, and whether the gender of the customer is a factor. Among 20 men who bought fireworks during a particular 2-hour period, 14 purchased from service organizations, the other 6 purchased from non-service groups. Of the 18 women who purchased in the same period, 8 bought from service organizations, and 10 from non-service groups. Is the gender of the purchaser related to the group from which the purchase is made?
6. A corporate CEO is interested in whether 20 management trainees’ possession of a graduate degree (yes/no) is related to their promotion within the first five years (yes/no). The X2 value is 8.450.
1. What does the X2 value indicate about possession of a graduate degree and promotion?
2. What is the value of ϕ?