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, we are 99% confident that the average number of rooms rented daily in a given month is somewhere between 246.36 and 493.64.

Question

Quizplus · Accepted Answer

This statement is true as we can use the formula for a confidence interval for a population mean, where:

confidence interval = sample mean ± (t-score)(standard error)

Assuming a 99% confidence level, with 24 degrees of freedom (n-1), the t-score will be 2.492. The standard error can be found using the formula:

standard error = (standard deviation)/√(sample size) = 240/√25 = 48

Plugging in the values, we get:

confidence interval = 370 ± (2.492)(48) = (246.36, 493.64)

Therefore, we can be 99% confident that the true population mean of rooms rented daily in a given month falls within this interval. This is a confidence interval problem and the formula to calculate the interval is:

sample mean ± z-score (critical value) x standard error

The standard error is calculated as the standard deviation divided by the square root of the sample size:

240 / sqrt(25) = 48

The critical value for a 99% confidence level and a sample size of 25 is 2.797.

So, the confidence interval is:

370 ± 2.797 x 48 = (246.36, 493.64)

Therefore, the statement is true.

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