You are given the sample mean and the population standard deviation. Use this in

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. If convenient use technology to construct the confidence intervals. A random sample of 60 home theater systems has a mean Price of $111.00. Assume the population standard deviation is $19.20. Construct a 90% confidence interval for the population mean. The 90% confidence interval is (106.93, 115.07) (Round to two decimal places as needed.) Construct a 95% confidence interval for the population mean. The 95% confidence interval is (Round to two decimal places as needed.)

Explanation / Answer

std error of mean =std deviation/(n)1/2 =2.4787

for 90% CI; z=1.645

hence 90% confidence interval =sample mean -/+ z*std error =106.92 ; 115.08

for 95% CI, z=1.96

hence 95% confidence interval =sample mean -/+ z*std error =106.14 ; 115.86

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