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?

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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