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 55 home theater systems has a mean price of ?$145.00. Assume the population standard deviation is ?$15.50. Construct a? 90% confidence interval for the population mean.

Answer 1

a)

90% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

145 - 1.645 * 15.5 / sqrt(55) < < 145 + 1.645 * 15.5 / sqrt(55)

141.5619 < < 148.4381

90% CI is ( 141.5619 , 148.4381)

Interpretation- We are 90% confident that the population mean is between 141.5619 and 148.4381.

b)

95% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

145 - 1.96 * 15.5 / sqrt(55) < < 145 + 1.96* 15.5 / sqrt(55)

140.9036 < < 149.0964

95% CI is ( 140.9036 , 149.0964)

Interpretation - We are 95% confident that population mean is between 140.9036 and 149.0964

From the two confidence intervals, 95% confidence interval is wider than 90% confidence interval.