Question

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

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.

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.

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