Question

Use the standard normal distribution or the​ t-distribution to construct a 90​% 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 14 mortgage​ institutions, the mean interest rate was 3.44​% and the standard deviation was 0.49​%. Assume the interest rates are normally distributed. Which distribution should be used to construct the confidence​ interval? select a choice below

A. Use a​ t-distribution because the interest rates are normally distributed and sigma is known.

B. Use a normal distribution because nless than30 and the interest rates are normally distributed.

C. Use a​ t-distribution because it is a random​ sample, sigma is​ unknown, and the interest rates are normally distributed.

D. Use a normal distribution because the interest rates are normally distributed and sigma is known.

E. Cannot use the standard normal distribution or the​ t-distribution because sigma is​ unknown, n less than 30​, and the interest rates are not normally distributed.

Select the correct choice below​ and, if​ necessary, fill in any answer boxes to complete your choice.

A. The 90​% confidence interval is ​( , ​). ​(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.With 90​%​confidence, it can be said that the population mean interest rate is between the bounds of the confidence interval.

B.It can be said that 90​% of institutions have an interest rate between the bounds of the confidence interval.

C.If a large sample of institutions are taken approximately 90​% of them will have an interest rate between the bounds of the confidence interval.

D.Neither distribution can be used to construct the confidence interval.

Click to select your answer.

Answer 1