SCENARIO 8-7
A hotel chain wants to estimate the mean number of rooms rented daily in a given month.The population of rooms rented daily is assumed to be normally distributed for each month with a standard deviation of 240 rooms.During February,a sample of 25 days has a sample mean of 370 rooms.
-Referring to Scenario 8-7,it is possible that the 99% confidence interval calculated from the data will not contain the sample mean number of rooms rented daily in a given month.

Question

Quizplus · Accepted Answer

Since the sample size is large enough (n=25) and the population standard deviation is known (240), we can use a z-test to calculate the confidence interval. The 99% confidence interval for the population mean is calculated to be (326.29, 413.71) using the formula:

sample mean ± z*(standard error)

where z is the 99% confidence level z-score (2.576) and the standard error is calculated as the population standard deviation divided by the square root of the sample size (240/√25=48).

Since the sample mean (370) is within the confidence interval, it is not possible for the interval to not contain the sample mean. Therefore, the answer is B (False).

SCENARIO 8-7 a Hotel Chain Wants to Estimate the Mean Number of Number