Question

Before agreeing to purchase a large order of polyethylene sheaths for a particular type of high-pressure oil-filled submarine power cable, a company wants to see conclusive evidence that the true standard deviation of sheath thickness is less than 0.05 mm. What hypotheses should be tested, and why

Answer 1

The company should test the null hypothesis that the true standard deviation of sheath thickness is at least 0.05 mm against the alternative hypothesis that it is less than 0.05 mm to ensure quality requirements are met.

Step-by-step explanation:

The company interested in purchasing polyethylene sheaths for high-pressure oil-filled submarine power cables must verify that the true standard deviation of sheath thickness is less than 0.05 mm. To do this, the company should set up a hypothesis test where the null hypothesis (H0) and the alternative hypothesis (Ha) would be as follows:

H0: σ ≥ 0.05 mm - The true standard deviation of sheath thickness is at least 0.05 mm.

Ha: σ < 0.05 mm - The true standard deviation of sheath thickness is less than 0.05 mm.

This test is necessary to provide evidence that the thickness consistency meets the company's quality requirements. A statistical test such as the chi-square test for variance might be used to assess the variability of the sheath thickness compared to the specified threshold.

Answer 2

Step-by-step explanation:

To help the company achieve a true standard deviation of sheath thickness is less than 0.05 mm, the company should test the hypothesis that

Null hypothesis: standard deviation of sheath thickness is greater than or equal to 0.05 mm

While the alternative hypothesis: standard deviation of sheath thickness is less than 0.05 mm.

Making such hypotheses enable us to be able to find conclusiveevidence against the null hypothesis to either reject or to fail to reject the null hypothesis