Problem I. 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 to high, it is one indication of financial instability. Banks often monitor the financial health of companies to which they have extended commercial loans. A "lean" debt-to-equity ratio is considered to be a ratio of 1.50. A particular bank ran an audit for its loan portfolio's debt-to-equity ratio and randomly selected a sample of 15 of its commercial loan accounts, producing the follow result: 1.32 1.27 1.45 1.67 1.73 1.49 1.59 1.09 1.26 1.78 1.36 1.65 1.54 1.69 1.38 The sample mean and standard deviation for above sample are, A. What is the point estimator of population mean, ? B. Find a 98% confidence interval for the bank's debt-to-equity ratio for its loan portfolio. C. Interpret the results you found in B. D. How would the confidence interval change if you had assumed that the population standard deviation was known to be 0.202? Problem II. A commercial processing plant fills containers with salted nuts. Machinery on the production line is set to maintain a standard deviation (i.e., population SD) of 0.08 ounces. A quality control officer takes random samples of 50 containers every 15 minutes and determined individual product weights. The last sample of 50 containers produced a mean of 5.8 ounces. A. What is the point estimator of population mean, ? B. Find a 90% confidence interval for the weight of the containers. C. Interpret the results you found in B. D. It is important to have not less than 5 ounces of nuts in a container due to FCC regulation. Using the 90 percent confidence interval, can the quality control officer be confident that u is larger than five ounces? Explain