Question

A manufacturer offers a 36-month warranty on a new line of its products. Production engineers believe the lifetime, Y, of any randomly selected item from this new line has a normal distribution with mean µ = 45 and standard deviation σ = 7. Accordingly, the probability an item fails within the first 36 months after purchase is

Thus, under typical conditions only about 10% of the items will fail early, and, since this percentage is so low, managers and marketers of the product consider it cost effective to replace such items. However, the rate of early failures will increase if either µ decreases or σ increases, and under the 36-month warranty policy, this would decrease revenues to the manufacturer. To investigate whether the early failure rate has increased, the manufacturer’s quality control team drew a random sample of n = 5 items and measured their lifetimes. These measurements (in months) are 37 54 29 46 33

Assume all measurements arise from a normal population

5.Create a Normal Quantile Plot for this analysis and upload the plot.

6. Comment on the normality assumptions based on the plot computed for Question 5.

7. Calculate the point estimate for the 90% confidence interval for the mean lifetime ?? (round answers to one decimal place).

8. Using software or a statistical table, find the critical value the for the 90% confidence interval for the mean lifetime ?? (round answers to 3 decimal places.)

9. Calculate the standard error for the 90% confidence interval for the mean lifetime ?? (round answers to one decimal place).

10. If instead of a 90% confidence interval, you calculated a 95% confidence interval. Would the 95% interval be wider or narrower than the 90% confidence interval you constructed in Questions 7-9?

a. Wider

b. Narrower

Answer 1