The tensile strength of a fiber used in manufacturing cloth is ofinterest to the

Question

The tensile strength of a fiber used in manufacturing cloth is ofinterest to the purchaser. Previous experience indicates that thestandard deviation of the tensile strength is 2 psi. A randomsample of 8 fiber specimens is selected and the average tensilestrength is found to be 127 psi.
a)Test the hypothesis that the mean tensile strength equals 125 vs.the alternative that the mean exceeds 125 psi, use alpha=.05
b)What is the p-value for this test?
c)discuss why a one sided alternative was chosen in a
d)construct a 95% lower confidence interval on the mean tensilestrength

Explanation / Answer

Because we are given the mean and standard deviation of thepopulation, we can use a z-test. Population = 125, = 2 Distribution of the sample means x_bar = 125, x_bar = 2/n =2 / 8 = 1/2 = 0.707 (a) Ho : 125 zcrit(=0.05 one tailed) = 1.64 zobs = (X_bar - x_bar) /x_bar= (127 - 125) / 0.707 = 2.828 zobs > zcrit Reject the null hypothesis, the mean is statisticallysignificantly greater than 125 b)What is the p-value for this test? p-value = 0.00234 c)discuss why a one sided alternative was chosen in a A one tailed test was chosen because we are testing a directionalhypothesis. d)construct a 95% lower confidence interval on the mean tensilestrength 95%CI = x_bar +/- x_bar * zcrit(=0.05, two tailed) = 127 +/- 0.707 * 1.96 Lower 95%CI = 125.61

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