Question

AM 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 35 home theater systems has a mean price of $144.00. Assume the population standard deviation is $15.60. Construct a 90% confidence interval for the population mean. The 90% confidence interval is (0-0). (Round to two decimal places as needed.) Construct a 95% confidence interval for the population mean. The 95% confidence interval is (0) (Round to two decimal places as needed.) Interpret the results. Choose the correct answer below. O 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 wider than the 90% OB. 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%. OC. 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% |AM AM Click to select your answers)

Answer 1

a)

We know that the 90% confidence interval for population mean is given by:

(+ Zo. 10/2. ( 4 Zo.05. 15.60, (144 + (1.645) (35 (144 +4.34) (139.66.148.34)

b)

We know that the 95% confidence interval for population mean is given by:

$\\(\overline{x}\pm Z_{0.05/2}\frac{\sigma}{\sqrt{n}})\\ \\ (\overline{x}\pm Z_{0.025}\frac{\sigma}{\sqrt{n}})\\ \\ (144\pm (1.96)\frac{15.60}{\sqrt{35}})\\ \\ (144\pm 5.17)\\ \\ (138.83,149.17)$

c)

So, with 90% confidence, it can be said that the population mean lies in 1st interval and with 95% confidence, it can be said that the population mean lies in 2nd interval. Also, 95% interval is wider than 90% interval.

Hence option A.