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 $137.00. Assume the population standard deviation is $16.60. Construct a 90% confidence interval for the population mean. The 90% confidence interval is (T ). (Round to two decimal places as needed.)

Explanation / Answer

100(1-alpha)% confidence interval is given by :

Upper limit = Mean + Zalpha/2 * ( S / n0.5 )

Lower limit = Mean - Zalpha/2 * ( S / n0.5 )

We are given, Mean = 137

n = sample size = 60

S = standard deviation = 16.60

Alpha = 1 - 0.90 = 0.10

Zalpha/2 = Z0.10/2 = Z0.05 = 1.645

90% confidence interval is :

Upper limit = 137 + 1.645 * ( 16.60 / 600.5 ) = 140.53

Lower limit = 137 - 1.645 * ( 16.60 / 600.5 ) = 133.47

90% confidence inetrval is : ( 133.47 , 140.53 )

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