A Supermarket Has Just Added a New Cash Register to Reduce

question 105

Essay

A supermarket has just added a new cash register to reduce the waiting times of the customers during weekends. Because a new cash register has been added, the customers expect their waiting time to be less than the waiting time had been before the cash register was added. Suppose the sample variance of the waiting times for 25 customers before adding the new cash register is = 4.8 minutes, while the sample variance of the waiting times for 25 customers after adding the cash register is = 2.2 minutes. The manager of the supermarket believes that the waiting times are normally distributed and that the two samples are drawn independently.
A) Develop the hypotheses to test whether the ratio of two population variances is less than 1.
B) Calculate the appropriate test statistic.
C) Using the p-value approach, what is the decision at the 5% significance level?
D) What is the conclusion? Given that all other criteria are satisfied, should the supermarket continue with the new cash register?

• A) Develop the hypotheses to test whether the ratio of two population variances is less than 1.
• B) Calculate the appropriate test statistic.
• C) Using the p-value approach, what is the decision at the 5% significance level?
• D) What is the conclusion? Given that all other criteria are satisfied, should the supermarket continue with the new cash register?

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Definitions:

Moral Hazard

The situation where one party in an agreement is tempted to take undue risks because the negative consequences of the risk will be suffered by the other party.

Efficient Level

The optimal point of production or operation where costs are minimized and productivity or utility is maximized.

Warranty

A guarantee, usually made by a seller to a buyer, promising to repair or replace a product if necessary within a specified period.

High Quality

The standard of something as measured against other similar things, indicating it is of superior grade.