Question

Use the standard normal distribution or the t distribution to construct a 9 % confidence interval for the population mean Justify your decision if neither distribution can be used, explain why Interpret the results ln a random sample of 17 mortgage institutions, the mean interest rate was 3.69% and the standard deviation was 36% Assume the iterest rates are normally distributed Which distribution should be used to construct the confidence interval? ○ A. Use a t-distribution because it is a random sample. σ is unknown, and the interest rates are normaly distributed O B. Use a normal distribution because the interest rates are normally distributed and ơ is known. О с. Use a normal distribution because n < 30 and the interest rates are normally distributed 0 D. Use a t-distribution because the interest rates are normally distributed and ơ is known ○ E. Cannot use the standard normal distrit ution or the t-distribution because σ is unknown, n < 30, and the interest rates are not normally distributed. Select the correct choice below and, if necessary, in any answer boxes to complete your choice. A. The 90% confidence interval is ruil) Round to two decimal places as needed) Neither distribution can be used to construct the confidence interval O B. Interpret the results. Choose the correct answer below A. If a large sample of institutions are taken approximately 90% of them wil have an interest rate between the bounds ofthe confidence interval O B. With 90% confidence, it can be said that the population mean interest rate is between the bounds of the confidence interval O c. It can be said that 90% of institutions have an interest rate between the bounds of the confidence interval O D. Neither distribution can be used to construct the confidence interval

Answer 1

1)option A is correct: use a t -distribution...

2)

option A: the 90% CI =3.54 ; 3.84

3)

option B is correct