Suppose a grocery store is considering the purchase of a newself-checkout machine that will get customers through the checkoutline faster than their current machine. Before he spends the moneyon the equipment, he wants to know how much faster the customerswill check out compared to the current machine. The store managerrecorded the checkout times, in seconds, for a randomly selectedsample of checkouts from each machine. The summary statistics areprovided in the table.
| Group | Description | Sample
size | Sample
mean (min) | Sample standard
deviation (min) | Standard error
estimate (min) |
|---|
| 1 | old machine | n1=51n1=51 | ¯¯¯x1=128.4x¯1=128.4 | s1=29.8s1=29.8 | SE1=4.17283SE1=4.17283 |
| 2 | new machine | n2=48n2=48 | ¯¯¯x2=113.0x¯2=113.0 | s2=24.2s2=24.2 | SE2=3.49297SE2=3.49297 |
df=94.99897df=94.99897
Compute the lower and upper limits of a 95% confidence intervalto estimate the difference of the mean checkout times for allcustomers. Estimate the difference for the old machine minus thenew machine, so that a positive result reflects faster checkouttimes with the new machine. Use the Satterthwaite approximatedegrees of freedom, 94.99897. Give your answers precise to at leastthree decimal places.
upper limit:
lower limit:
