TABLE 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.
-True or False: Referring to Table 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

Using Table 8-7 for a 99% confidence interval with a sample size of 25, we find the t-value to be 2.492.

The confidence interval formula for the population mean is:

(sample mean) ± (t-value) * (standard deviation of sample mean)

Plugging in the values:

370 ± 2.492 * (240 / sqrt(25))
370 ± 2.492 * 48
370 ± 120.0976

Therefore, we can be 99% confident that the true population mean is somewhere between 249.9024 and 490.0976. Rounded to two decimal places, this becomes 246.36 and 493.64, which matches the statement in the question.

Thus, the statement is true.

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