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 population standard deviation of sheath thickness is less than .05 mm. What hypotheses should be tested, and why

H0 : σ = 0.5

H0 : σ < 0.5

Step-by-step explanation:

From the scenario described above, the company wants to see conclusive evidence that the population standard deviation of sheath thickness is less than .05 mm ; THIS SIMPLY means ; REJECTION OF the NULL HYPOTHESIS. This is because once there is a significant or conclusive evidence in hypothesis testing, then we reject the null and support the claim of the alternative hypothesis.

Hence, the alternative hypothesis is ; population standard deviation of sheath Thickness is less than 0.5.

H1 : σ < 0.5 ;

Therefore, our null will be ;

H0 : σ = 0.5