Question

# You are given the sample mean and the population standard deviation. Use this information to construct...

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.

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.

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