Producer’s and consumer’s risk. In quality-control applications of hypothesis testing, the null and alternative hypotheses are frequently specified as H0: The production process is performing satisfactorily. Ha: The process is performing in an unsatisfactory manner. Accordingly, a is sometimes referred to as the producer’s risk, while b is called the consumer’s risk (Stevenson, Operations Management, 2018). An injection molder produces plastic golf tees. The process is designed to produce tees with a mean weight of .250 ounce. To investigate whether the injection molder is operating satisfactorily, 40 tees were randomly sampled from the last hour’s production. Their weights (in ounces) are listed in the following table. .247 .251 .254 .253 .253 .248 .253 .255 .256 .252 .253 .252 .253 .256 .254 .256 .252 .251 .253 .251 .253 .253 .248 .251 .253 .256 .254 .250 .254 .255 .249 .250 .254 .251 .251 .255 .251 .253 .252 .253

a. Write H0 and Ha in terms of the true mean weight of the golf tees, m.

b. Access the data and find x and s.

c. Calculate the test statistic.

d. Find the p-value for the test.

e. Locate the rejection region for the test using a = .01.

f. Do the data provide sufficient evidence to conclude that the process is not operating satisfactorily? TEES g. In the context of this problem, explain why it makes sense to call a the producer’s risk and b the consumer’s risk. Applying the Concepts—Intermediate