Before agreeing to purchase a large order of polyethylene sheaths for a particular type of high-pressure oilfilled submarine power cable, a company wants to see conclusive evidence that the true standard deviation of sheath thickness is less than .05 mm. What hypotheses should be tested, and why

H₀: σ ≥ 0.05 mm.

Hₐ: σ < 0.05 mm.

Step-by-step explanation:

A company is purchasing a large order of polyethylene sheaths for a particular type of high-pressure oil filled submarine power cable.

The company wants to be sure of the fact that the standard deviation of sheath thickness of the total population of power cable is less than 0.05 mm.

To confirm this the company should perform a hypothesis test for the significance of the population standard deviation.

The hypothesis for this test can be defined as:

H₀: The standard deviation of sheath thickness is not less than 0.05 mm, i.e. σ ≥ 0.05 mm.

Hₐ: The standard deviation of sheath thickness is less than 0.05 mm, i.e. σ < 0.05 mm.

The alternate hypothesis is the claim to tested.

And the null hypothesis is a null statement, i.e. a statement that should be rejected.

Since the company wants the standard deviation of sheath thickness to be less than 0.05 mm, it needs to reject the null hypothesis.