Question

use the standard normal distribution or the t - distribution to construct a 95% confidence interval for the population mean. justify your decision. if neither distribution can be used, explain why. interpret the results. in a random sample of 13 mortgage institutions, the mean interest rate was 3.48% and the standard deviation was 0.36%. assume the interest rates are normally distributed. a. the 95% confidence interval is (3.26, 3.70). (round to two decimal places as needed.) b. neither distribution can be used to construct the confidence interval. interpret the results. choose the correct answer below a. it can be said that 95% of institutions have an interest rate between the bounds of the confidence interval. b. if a large sample of institutions are taken approximately 95% of them will have an interest rate between the bounds of the confidence interval. c. with 95% confidence, it can be said that the population mean interest rate is between the bounds of the confidence interval. d. neither distribution can be used to construct the confidence interval.

Explanation:

A confidence interval for the population mean gives a range of values within which the population mean is likely to lie. The interpretation of a confidence interval is that with a certain level of confidence (in this case 95%), the population mean is within the bounds of the confidence interval. Option A and B wrongly refer to the proportion of institutions (individual data points) instead of the population mean. Option D is incorrect as the t - distribution can be used (small sample size \(n = 13\), population standard deviation unknown, and data is normally distributed).

Answer:

C. With 95% confidence, it can be said that the population mean interest rate is between the bounds of the confidence interval.