Question

5. A manufacturer claims that the mean tensile strength of thread A exceeds the average tensile strength of thread B. To test his claim, 16 sample pieces of each type of thread are tested under similar conditions. Type A thread had a sample average tensile strength of 185 kilograms with a standard deviation of 6 kilograms, while type B thread had a sample average tensile strength of 178 kilograms with a standard of 9 kilograms. Assume that both populations are normally distributed and the variances are equal. Use α=0.05.

(a) Is there evidence to support the claim? Use critical region(s) for testing. (5 pts)

(b) Calculate the P-value for the above test in part (a) and make a conclusion on the test. (5 pts)

(c) Construct an appropriate 95% bound for the difference in mean tensile strength between type A and type B, that is μA-μB to test the hypothesis. (5 pts)

(d) Test a claim that the mean tensile strength of type A thread is at least 15 kilograms higher than that of type B thread by using the interval constructed in part (c). (You need to explain why you come up to that conclusion) (5 pts)

Answer 1