Question

The marketing director of a large department store wants to estimate the average number of customers who enter the store every five minutes. She randomly selects five-minute intervals and counts the number of arrivals at the store. She obtains the figures 52, 32, 41, 49, 56, 80, 46, 29, 32, and 71. The analyst assumes the number of arrivals is normally distributed. Using these data, the analyst computes a 95% confidence interval to estimate the mean value for all five-minute intervals. What interval values does she get?

(Round the intermediate values to 2 decimal places. Round your answers to 2 decimal places.)

Answer 1

It is given that:

The marketing director of a large department store wants to estimate the average number of customers who enter the store every five minutes. She randomly selects five-minute intervals and counts the number of arrivals at the store. She obtains the figures 52, 32, 41, 49, 56, 80, 46, 29, 32, and 71. The analyst assumes the number of arrivals is normally distributed.

The sample size is .

The sample mean is obtained as:

The sample standard deviation is obtained as:

The analyst assumes the number of arrivals (population) is normally distributed and the population standard deviation is unkwown.

The level of confidence is given as:

The level of significance can be obtained as:

The critical value that should be used in constructing the confidence interval for population mean is based on t-distribution as the population standard deviation is unknown.

Therefore, its value can be obtained using statistical tables as:

The formula to construct the 95% confidence interval to estimate the mean value for all five-minute intervals is:

The lower endpoint of the interval is:

The upper endpoint of the interval is:

Therefore, the 95% confidence interval to estimate the mean value for all five-minute intervals is .