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. From a random sample of 33 business​ days, the mean closing price of a certain stock was ​$111.13. Assume the population standard deviation is ​$10.41. The​ 90% confidence interval is ​( nothing​, nothing​). ​(Round to two decimal places as​ needed.) The​ 95% confidence interval is ​( nothing​, nothing​). ​(Round to two decimal places as​ needed.) Which interval is​ wider? Choose the correct answer below. The​ 90% confidence interval The​ 95% confidence interval Interpret the results. A. You can be certain that the closing price of the stock was within the​ 90% confidence interval for approximately 30 of the 33 ​days, and was within the​ 95% confidence interval for approximately 31 of the 33 days. B. You can be​ 90% confident that the population mean price of the stock is between the bounds of the​ 90% confidence​ interval, and​ 95% confident for the​ 95% interval. C. You can be certain that the population mean price of the stock is either between the lower bounds of the​ 90% and​ 95% confidence intervals or the upper bounds of the​ 90% and​ 95% confidence intervals. D. You can be​ 90% confident that the population mean price of the stock is outside the bounds of the​ 90% confidence​ interval, and​ 95% confident for the​ 95% interval. Click to select your answer(s). please answer the all parts of the question please.

Answer 1

The statistical software output for this problem is:

Hence,

a) 90% confidence interval: (108.15, 114.11)

b) 95% confidence interval: (107.58, 114.68)

c) The 95% confidence interval is wider.

d) You can be​ 90% confident that the population mean price of the stock is between the bounds of the​ 90% confidence​ interval, and​ 95% confident for the​ 95% interval. Option B is correct.