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 59 ​dates, the mean record high daily temperature in a certain city has a mean of 86.32degrees°F. Assume the population standard deviation is 14.97degrees°F.   The​ 90% confidence interval is ​(). ​(Round to two decimal places as​ needed.)   The​ 95% confidence interval is ​(). ​(Round to two decimal places as​ needed.)   Which interval is​ wider? Choose the correct answer below. A) The​ 90% confidence interval   B) The​ 95% confidence interval   Interpret the results.     A. 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.   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 certain that the mean record high temperature was within the​ 90% confidence interval for approximately 53 of the 59 ​days, and was within the​ 95% confidence interval for approximately 56 of the 59 days.

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
59
​dates, the mean record high daily temperature in a certain city has a mean of
86.32degrees°F.
Assume the population standard deviation is
14.97degrees°F.
 
The​ 90% confidence interval is
​().
​(Round to two decimal places as​ needed.)
 
The​ 95% confidence interval is
​().
​(Round to two decimal places as​ needed.)
 
Which interval is​ wider? Choose the correct answer below.
A) The​ 90% confidence interval
 
B) The​ 95% confidence interval
 
Interpret the results.
 
 
A.
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.
 
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 certain that the mean record high temperature was within the​ 90% confidence interval for approximately
53
of the
59
​days, and was within the​ 95% confidence interval for approximately
56
of the
59
days.

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