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Suppose that you are the manager of a restaurant for a fast-food franchise. Last month, the mean waiting time at the drive-through window was 3.70...

Suppose that you are the manager of a restaurant for a fast-food franchise. Last month, the
mean waiting time at the drive-through window was 3.70 minutes. After you follow the franchise’s
instruction to reduce the customers’ waiting time, you want to see if it is actually improved. To do
so, you select a random sample of 50 orders. The sample mean of waiting time is 3.75 minutes, with
a standard deviation of 0.8 minutes.
(1) Find a test statistics.
(2) At the 10% level of significance, is there evidence that the franchise’s instruction helps you reduce
the customers’ waiting time?
Question 3
A manufacturer of baseballs need to produce the balls with accurate diameter to meet its official
size provided by the Major League Baseball. Therefore, it needs a small number in the variance of the
diameters of balls, and a engineer claim that its variance is exactly .010 inches. You select 20 balls
from the factory, and found that the variance is .012 inches.
(1) Find a test statistics.
(2) At the 5% level of significance, is the claim correct?
Question 4
A manufacturer of chocolate candies uses machines to package candies. Although the packages are
labeled as 8 ounces, the company wants the packages to contain 8.17 ounces so that virtually none of
the packages contains less than 8 ounces. A sample of 15 packages are selected to see if the package
contains exactly 8.17 ounces on average. Suppose that such sample has a mean of 8.10 ounces, with
a standard deviation of 0.10 ounces.
(1) Find a test statistics.
(2) At the 1% level of significance, is there evidence that the population mean is exactly 8.17 ounces?

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