Question

Issue 4: Design a Guarantee Policy

A company developed a new product – Toner Cartridge. In order to attract more customers to purchase the new product, the manager of the company designs a guarantee policy. If a customer purchases a toner cartridge that does not reach the guaranteed pages, the customer can get 50% of the money back. The manager does not want to lose money. However, if the guaranteed pages were set too low, the guarantee policy will not be attractive to customers at all. From actual tests with the toner cartridges, the company estimated that the mean of printing pages is 30,000 pages and the standard deviation is 1500 pages. To determine guaranteed pages, the manager just simply sets 28,500 pages as guaranteed pages. In your opinion, does the way the manager determines the guaranteed pages make any sense? If you think that it does, explain your reason why. If not, explain your reason why not, and describe what you would do if you were the manager. Discuss and explain your reasons. You must provide your statistical analysis and reasons.

Answer 1

The company estimated mean pages as 30000 and standard deviation as 1500.

To test whether the managers decision is right or not let us conduct a statistical test

H₀: or

H_A:

Let the sample size be 100.

If the sample size is any number between 4 or more we get the calculated value of Z will be greater than or equal to 2.

Z critical value = -1.96

Hence we accept H₀, and conclude that the mean number of pages is greater than or equal to 28500.

Thus the manager's decision makes sense.

In my opinion manager can keep the guaranteed number of pages more.

If he keeps the guaranteed pages maximum as 30295 to attract the customers

In this case in the above calculation, we get the value of Z slightly greater than -1.96 and we accept H₀ at 5% level of significance.

But if he guarantees more than 30295 he will loose money on the product 95% of the times.