Question

Suppose a grocery store is considering the purchase of a new self-checkout machine that will get customers through the checkout line faster than their current machine. Before he spends the money on the equipment, he wants to know how much faster the customers will check out compared to the current machine. The store manager recorded the checkout times, in seconds, for a randomly selected sample of checkouts from each machine. The summary statistics are provided in the table.

Group	Description	Sample size	Sample mean	SampleStandard Deviation	StandardErrorEst
1	Old Machine	?1=49	?⎯⎯⎯1=126.4	?1=27.8	SE1=3.97143
2	New machine	?2=46	?⎯⎯⎯2=111.0	?2=22.2	SE2=3.27321

Compute the lower and upper limits of a 95% confidence interval to estimate the difference of the mean checkout times for all customers. Estimate the difference for the old machine minus the new machine, so that a positive result reflects faster checkout times with the new machine. Use the Satterthwaite approximate degrees of freedom, 90.71233. Give your answers precise to at least three decimal places.

upper limit: ____

lower limit: _____

Determine the meaning of the lower and upper limits of the confidence interval.

A.) The store manager is 95% confident that the difference in the mean checkout time of all customers using the new machine compared to the current one is contained in the calculated interval.

B.)The store manager is 95% confident that the mean difference in checkout times for all customers using the new machine compared to the current one is contained in the calculated interval.

C.) The probability is 95% that the difference in the mean checkout time of all customters using the new machine compared to the old one is within the bounds of the confidence interval. The probability is 95% that the mean difference in checkout times for all customers using the new machine compared to the current one is contained in the calculated interval.

Answer 1