Question

A company is evaluating suppliers for polyethylene sheaths for a particular type of high-pressure oil-filled submarine power cable. They want to see solid evidence that the true standard deviation of sheath thickness is less than 0.05 mm.

(a) Set up the null and alternative hypothesis.

(b) Describe a Type 1 and Type 2 error in this situation. Your answer should be in context of the problem.

Answer 1

Part a

Null hypothesis: H0: The true standard deviation of sheath thickness is 0.05 mm.

Alternative hypothesis: Ha: The true standard deviation of sheath thickness is less than 0.05 mm.

H0: σ = 0.05 versus Ha: σ < 0.05

This is a lower or left tailed test.

Part b

The type I error occurred when we conclude that the true standard deviation of sheath thickness is less than 0.05 mm, however, in fact, the true standard deviation of sheath thickness is 0.05 mm.

The type II error occurred when we conclude that the true standard deviation of sheath thickness is 0.05 mm, however, in fact, the true standard deviation of sheath thickness is less than 0.05 mm.