Question

# You are given the sample mean and the sample standard deviation. Use this information to construct...

You are given the sample mean and the sample 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 5050 home theater systems has a mean price of ​\$145.00145.00 and a standard deviation is ​\$18.7018.70.

The​ 90% confidence interval is

The​ 95% confidence interval is

Interpret the results. Choose the correct answer below.

A.

With​ 90% confidence, it can be said that the population mean price lies in the first interval. With​ 95% confidence, it can be said that the population mean price lies in the second interval. The​ 95% confidence interval is narrower than the​ 90%.

B.

With​ 90% confidence, it can be said that the sample mean price lies in the first interval. With​ 95% confidence, it can be said that the sample mean price lies in the second interval. The​ 95% confidence interval is wider than the​ 90%.

C.

With​ 90% confidence, it can be said that the population mean price lies in the first interval. With​ 95% confidence, it can be said that the population mean price lies in the second interval. The​ 95% confidence interval is wider than the​ 90%.

The statistical software output for this problem is:

Hence,

90% confidence interval: (140.57, 149.43)

95% confidence interval: (139.69, 150.31)

With​ 90% confidence, it can be said that the population mean price lies in the first interval. With​ 95% confidence, it can be said that the population mean price lies in the second interval. The​ 95% confidence interval is wider than the​ 90%. Option C is correct.

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