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 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.

#### Homework Answers

Answer #1

1)

 sample mean 'x̄= 82.8 sample size    n= 72 std deviation σ= 15.25 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.

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