# Question

Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches long. The machine that makes these rods does not produce each rod exactly 36 inches long. The lengths of the rods are normally distributed, and they vary slightly. It is known that when the machine is working properly, the mean length of the rods is 36 inches. The standard deviation of the lengths of all rods produced on this machine is always equal to .035 inch. The quality control department at the company takes a sample of 20 such rods every week, calculates the mean length of these rods, and tests the null hypothesis µ = 36, inches, against the alternative hypothesis, µ = 36 inches. If the null hypothesis is rejected, the machine is stopped and adjusted. A recent sample of 20 rods produced a mean length of 36.015 inches.

a. Calculate the p-value for this test of hypothesis. Based on this p-value, will the quality control inspector decide to stop the machine and adjust it if he chooses the maximum probability of a Type I error to be .02? What if the maximum probability of a Type I error is .10?

b. Test the hypothesis of part a using the critical-value approach and α = .02. Does the machine need to be adjusted? What if α = .10?

a. Calculate the p-value for this test of hypothesis. Based on this p-value, will the quality control inspector decide to stop the machine and adjust it if he chooses the maximum probability of a Type I error to be .02? What if the maximum probability of a Type I error is .10?

b. Test the hypothesis of part a using the critical-value approach and α = .02. Does the machine need to be adjusted? What if α = .10?

## Answer to relevant Questions

At Farmer’s Dairy, a machine is set to fill 32-ounce milk cartons. However, this machine does not put exactly 32 ounces of milk into each carton; the amount varies slightly from carton to carton but has a normal ...A company claims that the mean net weight of the contents of its All Taste cereal boxes is at least 18 ounces. Suppose you want to test whether or not the claim of the company is true. Explain briefly how you would conduct ...Consider the null hypothesis H0: µ = 100. Suppose that a random sample of 35 observations is taken from this population to perform this test. Using a significance level of .01, show the rejection and non-rejection regions ...The president of a university claims that the mean time spent partying by all students at this university is not more than 7 hours per week. A random sample of 40 students taken from this university showed that they spent an ...The past records of a supermarket show that its customers spend an average of $95 per visit at this store. Recently the management of the store initiated a promotional campaign according to which each customer receives ...Post your question

0