2. Debt-to-Equity Ratio. One measure of a company's financial health is its debt-to-equity ratio. This quantity is defined to be the ratio of the company's corporate debt to the company's equity. If this ratio is too high, it is one indication of financial instability. For obvious reasons, banks often monitor the financial health of companies to which they have extended commercial loans. Suppose that, in order to reduce risk, Loans-R-Us has decided to initiate a policy limiting mean debt-to-equity ratio for its portfolio of commercial loans to being less than 1.5. In order to estimate the mean debt-to-equity ratio of its current commercial loan portfolio, the bank randomly selects a sample of 15 of its commercial loan accounts. Audits of these 15 companies sampled result in the following debt-to-loan ratios: 1.41 1.15 1.45 1.21 1.19 1.87 1.37 1.41 1 1.22 1.21 1.46 1.23 1.39 1.32 1.55 a. What is the parameter Loans-R-Us wishes to estimate? b. Find a 96% confidence interval. c. Interpret this confidence interval in the context of the problem. English (United States) Focus E -d. Based on the interval, is Loans-R-Us in compliance with its new policy? 3. Humor in Television Ads. In the Journal of Advertising, the use of humor in television ads in the United States was compared with the use of humor in television ads in the United Kingdom. It was found that a substantially greater percentage of U.K. ads use humor. a) Suppose that a random sample of 400 television ads in the United Kingdom reveals that 194 of these ads use humor. i. What is the parameter? ii. Find p: iii. Construct a 95% confidence interval for this parameter. iv. Interpret this confidence interval in the context of the problem. English (United States) Focus E -b) Suppose a random sample of 500 television ads in the United States reveals that 122 of these ads use humor. i. What is the parameter? ii. Find p: iii. Construct a 95% confidence interval for this parameter. iv. Interpret this confidence interval in the context of the problem. c) Do the confidence intervals you computed in a) and b) suggest that a greater percentage of U.K. ads use humor? Explain. How might an ad agency use this information? English (United States) Focus E -c) Do the confidence intervals you computed in a) and b) suggest that a greater percentage of U.K. ads use humor? Explain. How might an ad agency use this information? d) Determine the sample size needed in order to be 90% confident that the sample proportion of ads using humor in the United Kingdom is within .04 of p. (based on the above approximation for p) e) Determine the sample size needed in order to be 90% confident that the sample proportion of ads using humor is within 0.04 of p. (suppose you do not have an approximation for p) English (United States) Focus E
