A manufacture claims that the average tensile strength of thread A exceeds the a

Question

A manufacture claims that the average tensile strength of thread A exceeds the average tensile strength of thread B by at least 13 kilograms. To test this claim. 50 pieces of each type of thread were tested under similar of conditions. Type A thread had an strength tensile strength of 89.2 kilograms with a standard deviation of 6.68 kilograms, while type B thread had an average tensile strength of 79.6 kilograms with a standard deviation of 5.86 kilograms. Test the manufacturer's claim using a 0.05 level of significance. Do not assume that the population variances are equal. Let type A thread correspond to population 1 and let type B thread correspond to population 2. Identify the null and alternative hypotheses. Choose the correct answer below. H_0: mu_1 - mu_2 t'

Explanation / Answer

df = [(n1-1)(n2-1)]/[(n2-1)(C2) + (1-C)2(n1-1)], C = (s12/n1)/((s12/n1)+(s22/n2)) = (6.682/50)/((6.682/50)+(5.862/50))
C = 0.5651123325, df = [(49)(49)]/[(49)(0.565112)+(1-0.56511)2(49)] = 96.37 = 96
For = 0.05, critical region is t' > 1.661

t = (x1 - x2)/sqrt((s12/n1)+(s22/n2)) = (89.2 - 79.6)/sqrt((6.682/50)+(5.862/50)) = 7.639

Since t > t', the result is significant and null hypothesis is rejected. We have sufficient evidence to suggest that thread A has higher average tensile strength than thread B.

Thread A Thread B N 50 50 Mean 89.2 79.6 Std. Dev. 6.68 5.86

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