# Test of hypothesis

1. The recent boom in sales of travel books has led to the marketing of other travel related guides, such as video travel guides and audio walking tour tapes. Barnes and noble has been studying the market for these travel guides. In one market test, a random sample of 25 potential travelers was asked to rate audiotapes of a certain destination, and another random sample of 20 potential travelers was asked to rate videotapes of the same destination. Both ratings were on a scale of 0 to 100 and measured the potential travelers' satisfaction with the travel guide they tested and the degree of possible purchase intent (with 100 the highest). The mean score for the audio group was 87, and their standard deviation was 12. The mean score for the video group was 64, and their standard deviation was 23. Do these data present evidence that one form of travel guide is better than the other? Advise barnes and noble on a possible marketing decision to be made.

2. According to High Times Journal, the home office is fast becoming a way of life for millions of Americans, and the cost of maintaining a home office is dropping. In 1995, the average initial investment in setting up a home office (buying a computer. printer, fax machine, was $3,300, according to the Journal.' Assume that this is based on a random sample of 50 home offices set up in 1995 and that the standard deviation was $ 1,000. Corresponding figures for 50 home offices set up in 1990 were average cost $5,200 and standard deviation $1,000. Test for a reduction in cost from 1990 to 1995.

3. Authors T. Peters and R. Waterman state in their book that the giant advertising firm of Johnson and Martin is more concerned with customer satisfaction than it is with company profits. Suppose a test is carried out to determine whether or not new management decisions at Johnson and Martin increase average customer satisfaction. To test this claim, a random sample of company clients is polled before an important management decision, and customer satisfaction is measured for this sample on a scale of I to 10. Then, some time after the management decision has been made and a new company policy implemented, another sample of clients is polled, and their satisfaction scores are computed (on the same scale). Letting the subscript b denoted "before the new decision" and the subscript a denoted "after the new decision," the results of the surveys are: Using these data, do you believe that customer satisfaction is increased, on the average, after the new management decision and the resulting new company policy?

4. Stock price of a company was studied by using three independent variables and 50 observation. Attached results are obtained from the regression analysis. Draw a conclusion about the model and make a recommendation. Also, construct a 95% confidence interval for the regression coefficient for the variable -1.

Coefficients Standard errors.

Intercept 1.24 0.56

Variable -1 3.24 1.2

Variable -2 1.02 1.34

Variable -3 2.04 0.67

5. A study was conducted to determine whether a correlation exists between consumer's perceptions on TV commercial (measured on special scale) and their interest in purchasing the product (measured on a scale). The results are n=65, r=0.37. Is there statistical evidence (at 0.05 level of significance) of a linear correlation between the two variables?

6. The Fidelity Overseas mutual fund consists of about equal proportions of Japanese and European stocks. The percentage of the fund invested in any individual country varies according to prevailing rates of return on stocks in different countries. At the end of October 1995, the fund manager was considering the possibility of shifting the proportions invested in French, Dutch, and Italian stocks. This change would be made if it could be statistically substantiated that differences in average annualized rates of return during the period ending in October existed among stocks from the three countries. Random samples of 50 French stocks, 32 Dutch stocks, and 28 Italian stocks were collected, and the annualized rate of return for each stock over the period under study was computed. Then an analysis of variance was carried out, which produced the following results: SSE (Sum of square Error) = 22,399.8 and TSS (total sum of squares) = 32,156. 1. Based on these results, should the manager shift the proportions of the fund invested in the three countries? How confident are you of your answer? Construct a complete ANOVA table for this problem.

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#### Solution Summary

Answers questions on test of hypothesis, confidence interval etc.