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 72 ​dates, the mean record high daily temperature in a certain city has a mean of 82.80⁰F. Assume the population standard deviation is 15.25⁰F.

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. The​ 90% confidence interval The​ 95% confidence interval Interpret the results.

A. 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.

B. 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. C. 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.

D. You can be certain that the mean record high temperature was within the​ 90% confidence interval for approximately 65 of the 72 ​days, and was within the​ 95% confidence interval for approximately 68 of the 72 days.

Answer 1

1)

sample mean 'x̄=		82.800
sample size    n=		72
std deviation σ=		15.250
std error ='σx=σ/√n=15.25/√72=		1.7972

for 90 % CI value of z=		1.645
margin of error E=z*std error =		2.956
lower bound=sample mean-E=		79.844
Upper bound=sample mean+E=		85.756
from above 90% confidence interval for population mean =(79.84,85.76)

as above:

95% confidence interval for population mean =(79.28,86.32)

C. 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.