# Hypothesis Testing, Rank Correlation & Seasonality Index

11-59. Marketers know that tastes differ in various regions of the country. In the rental car business, an industry expert has given the opinion that there are strong regional preferences for size of car and quotes the following data in support of that view:

Region of Country

Preferred Car type Northeast Southeast Northwest Southwest

Full-size 105 120 105 70

Intermediate 120 100 130 150

All other 25 30 15 30

(a) State the appropriate null and alternative hypotheses.

(b) Do the data support the expert's opinion at the 0.05 significance level?

(c) What about at the 0.20 significance level?

11-67. An investor is interested in seeing whether there are significant differences in the rates of return on stocks, bonds and mutual funds. He has taken random samples of each type of investment and has recorded the following data.

Rate of Return (Percent)

Stocks 2.0 6.0 2.0 2.1 6.2 2.9

Bonds 4.0 3.1 2.2 5.3 5.9

Mutual funds 3.5 3.1 2.9 6.0

(a) State null and alternative hypotheses.

(b) Test your hypotheses at the 0.05 significance level.

(c) State an explicit conclusion.

11-80. In the development of new drugs for the treatment of anxiety, it is important to check the drugs' effects on various motor functions, one of which is driving. The Confab Pharmaceutical Company is testing four different tranquilizing drugs for their effects on driving skill. Subjects take a simulated driving test, and their scores reflect their errors. More severe errors lead to higher scores. The results of these tests produced the following table:

Drug 1 245 258 239 241

Drug 2 277 276 263 274

Drug 3 215 232 225 247 226

Drug 4 241 253 237 246 240

At the 0.05 level of significance, do the four drugs affect driving skill differently?

Business Week and U.S. News & World Report publish ranking of the top 20 business schools. The Business Week overall ranking is based on rankings obtained from students and from firms that recruit MBAs. Along with the rankings, the magazines report information about the cost of getting an MBA degree and the graduates' average starting salaries. Use the data in Table RW 12-1 to answer exercises 12-49 to 12-52.

1992 Rank BWRanking Starting

School BW USN&WR by Students by Firms Cost Salary

Northwestern 1 4 3 1 37,600 70,200

Chicago 2 6 10 4 38,500 68,600

Harvard 3 2 12 3 37,100 84,960

Wharton 4 3 15 2 37,600 72,200

Michigan 5 7 9 6 37,200 58,110

Dartmouth 6 10 1 12 37,500 74,260

Stanford 7 1 5 7 38,480 82,860

Indiana 8 18 6 8 24,600 49,070

Columbia 9 8 18 5 38,000 66,620

North Carolina 10 16 8 11 17,360 55,500

Virginia 11 11 2 15 28,500 65,280

Duke 12 9 7 14 37,000 59,870

MIT 13 5 14 10 39,000 73,000

Cornell 14 12 4 17 37,000 59,940

NYU 15 17 16 13 36,100 56,730

UCLA 16 14 11 16 22,500 64,540

Carnegie-Mellon 17 15 23 9 37,200 56,980

Berkeley 18 13 13 19 15,400 65,500

Vanderbilt 19 19 19 20 35,000 47,320

Washington 20 20 24 18 33,500 48,200

12-49. Plot a scatter diagram of the USN & WR ranking vs. The cost of the MBA degree. Do more expensive schools appear to get higher rankings? Calculate the sample coefficient of correlation between these two variables.

12-50. Is there a payoff for spending more on an MBA degree? Plot a scatter diagram of starting salary Vs. cost. Fit a regression equation to the data and test appropriate hypotheses about its slope.

12-51. Do graduates from the higher ranking schools get higher starting salaries? Plot scatter diagram of starting salary Vs. the Business Week overall ranking. Fit a regression equation to the data and test appropriate hypotheses about its slope.

12-52. How strongly are the starting salaries related to the rankings? Calculate the sample coefficients of determination between the starting salaries and the three Business Week rankings (overall, by students, and by firms). Which of these rankings explains the largest fraction of the variation in starting salaries?

14-71 Kruskal Wallis test (Please see the attachment)

14-78. Rank correlation coefficient (Please see the attachment)

15-60 RJ's Grocers has added broiled whole chickens to its line of takeout food for busy professionals who don't have time to cook at home. The number of precooked chickens sold in the first 7 weeks is as follows:

Week 1 2 3 4 5 6 7

Sales 41 52 79 76 72 59 41

(a) Find the linear regression line that best fits these data.

(b) Estimate the expected number of sales for week 8.

(c) Based on the estimate in part (b) and the available data, does the regression accurately describe the sales trend for this item?

15-44. Please see the attachment

(a). Calculate the seasonal indices for these data (use a 4-quarter centered moving average).

b). depersonalize these data using the indices from part (a).

c). Find the least-squares line that best describes the trend of the deseasonalized figures.

See attached file.

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#### Solution Summary

The solution provides step by step method for the calculation of test statistic for Chi square, Anova, Kruskal Wallis test and regression coefficient. The solution also provides step by step method for the calculation of rank correlation coefficient, seasonality index, correlation coefficient and regression equation. 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.