Use the standard normal distribution or the t-distribution to construct a 99 % c

Question

Use the standard normal distribution or the t-distribution to construct a 99 % confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 20 people, the mean length of stay at a hospital was 7.6 days. Assume the population standard deviation is 1.8 days and the lengths of stay are normally distributed. Which distribution should be used to construct the confidence interval?

A. Use a t-distribution because nless than 30 and sigma is unknown.

B. Use a normal distribution because ngreater than or equals 30.

C. Use a normal distribution because the lengths are normally distributed and sigma is known.

D. Use a t-distribution because the lengths are normally distributed and sigma is known.

E. Cannot use the standard normal distribution or the t-distribution because sigma is unknown, n less than 30 , and the days are not normally distributed.

Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice.

A. The 99 % confidence interval is (____,___ ). (Round to one decimal place as needed.)

B. Neither distribution can be used to construct the confidence interval. Interpret the results.

Choose the correct answer below.

A. With 99% confidence, it can be said that the population mean length of stay is between the bounds of the confidence interval.

B. If a large sample of patients are taken approximately 99% of them will have lengths of stay between the bounds of the confidence interval.

C. It can be said that 99% of patients have a length of stay between the bounds of the confidence interval.

D. Neither distribution can be used to construct the confidence interval.

Explanation / Answer

1)Use a normal distribution because the lengths are normally distributed and the population variance is known.

2)Z(99% CI)=2.576

sd(mean)=1.8/sqrt(20)=0.4025

CI=(7.6-2.576*0.4025,7.6-2.576*0.4025)=(6.6,8.6)

3)Hence with 99% confidence,it can be said that the poplation mean length of stay is between the bounds of the confidence interval.

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