Question

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.

From a random sample of

78

​dates, the mean record high daily temperature in a certain city has a mean of

85.43 degrees°F.

Assume the population standard deviation is

13.72 degrees°F.

The​ 90% confidence interval is

​(nothing​,nothing​).

​(Round to two decimal places as​ needed.)

The​ 95% confidence interval is

​(nothing​,nothing​).

​(Round to two decimal places as​ needed.)

Which interval is​ wider? Choose the correct answer below.

The​ 90% confidence interval

The​ 95% confidence interval

Interpret the results.

A.You can be certain that the mean record high temperature was within the​ 90% confidence interval for approximately

70

of the

78

​days, and was within the​ 95% confidence interval for approximately

74

of the

78

days.

B.

You can be certain that the population mean record high temperature is either between the lower bounds of the​ 90% and​ 95% confidence intervals or the upper bounds of the​ 90% and​ 95% confidence intervals.

C.

You can be​ 90% confident that the population mean record high temperature is outside the bounds of the​ 90% confidence​ interval, and​ 95% confident for the​95% interval.

D.

You can be​ 90% confident that the population mean record high temperature is between the bounds of the​ 90% confidence​ interval, and​ 95% confident for the​95% interval.

Answer 1

Which interval is​ wider?

You can be​ 90% confident that the population mean record high temperature is between the bounds of the​ 90% confidence​ interval, and​ 95% confident for the​ 95% interval.