Before agreeing to purchase a large order of polyethylene sheaths for a particulartype of high-pressure oil-?lled submarine power cable, a company wantsto see conclusive evidence that the mean of sheath thickness is less than :05mm. Assume the sheath thickness follows a normal distribution N(; 2); with unknown, and 2 = 2:25:Suppose 25 samples are obtained. And the sample mean X = 0:02:a) What test should you perform, that is, what are you null and alternativehypotheses?b) What test statistic you should use? Could you calculate the observedvalue of your test statistic?c) If we want to do the test at a signi?cance level 0.05, do you think thissample gives you enough con?dence to draw the conclusion that the mean ofsheath thickness is less than :05 mm? Show me your reason.d) Perform the same test using = 0:1 by ?rst computing the P-value andthen comparing it with the given sig. level :
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