A random sample of ten corporate analysts was asked to rate, on a scale from ( poor) to 10 (very high), the prospects for their own corporations and for the econom large in the current year. The results obtained are shown in the accompanying table. U the Wilcoxon test, discuss the proposition that in the aggregate, corporate analysts) more optimistic about the prospect for their own companies than for the economy at la 1. A professor is planning to use a new book for a financial accounting course and is consid- ering three possibilities: Financial Accounting Made Easy, Financial Accounting Without Tears, and Financial Accounting for Profit and Pleasure. He contacted a random sample. of sixty students who had already taken his course and asked each to review the three books, indicating a first preference. The results obtained are shown in the table. Test the null hypothesis that for this population, first preferences are evenly distributed over the three books.

2. A random sample of sixty-five mutual funds whose performance ranked in the top 25% of all funds in 1979 83 was selected. Their performance was observed over the next five years. In this later period, eleven of the sample funds ranked in the top 25% of all funds, seventeen in the second 25%, eighteen in the third 25%, and nineteen in the bottom 25%. Test the null hypothesis that a randomly chosen top 25% fund from 1979-83 is equally likely to fall into each of the four possible categories (performance quartiles) over the fol lowing five years. 3. A random sample of 502 consumers were asked about the importance of price as a factor in choosing a hospital." Sample members were asked to select "not important." "impor tant," or "very important" as an answer. Respective numbers selecting these answers were 169, 136, and 197. Test the null hypothesis that a randomly chosen consumer is equally likely to select each of these three answers. 4. Production records indicate that in normal operation for a certain electronic component, 93% have no faults, 5% have one fault, and 2% have more than one fault. For a random sample of 500 of these components from a week's output, 458 were found to have no faults, thirty to have one fault, and twelve to have more than one fault. Test at the 5% level the null hypothesis that the quality of the output from this week conforms to the usual pattem. 5. A charity solicits donations by telephone. It has been found that 60% of all calls result in a refusal to donate, 30% result in a request for more information through the mail, with at promise to at least consider donating; and 10% generate an immediate credit card dona- tion. For a random sample of 100 calls made in the current week, sixty-five resulted in a refusal to donate, thirty-one in a request for more information through the mail, and four in an immediate credit card donation. Test at the 10%-level the null hypothesis that the usual pattern of outcomes is being followed in the current week. 6. A campus administrator has found that 60% of all students view courses as very useful, 20% as somewhat useful, and 20% as worthless. Of a random sample of 100 students tak- ing business courses, sixty-eight found the course in question very useful, eighteen some- what useful, and fourteen worthless. Test the null hypothesis that the population distribu- tion for business courses is the same as that for all courses.