An engineer wants to check whether the average circumference of a certain type of rod

is less than 34.5 cm. He selects a random sample of 15 rods and finds that the

The average of this sample is 34.09 cm with a sample standard deviation equal to 0.42 cm.

(a) Formulate the null hypothesis and the alternative hypothesis that this engineer must test.

(b) Assuming that the circumference of this type of rod is normally distributed. Make

the test based on the rejection region rule. Give your conclusion with a threshold of

meaning = 0.01.

(c) Calculate the value P associated with the test done in (b). Give your conclusion with a threshold of

meaning = 0.01.