The breaking strengths of cables produced by a certain manufacturer have a mean,

Question

The breaking strengths of cables produced by a certain manufacturer have a mean, mu, of 1950 pounds, and a standard deviation of 100 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 50 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1963 pounds. Can we support, at the 0.01 level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed.) Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas.) The null hypothesis: H_0: The alternative hypothesis: H_1: The type of test statistic: The value of the test statistic: (Round to at least three decimal places.) The critical value at the 0.01 level of significance: (Round to at least three decimal places) Can we support the claim that the mean breaking strength has increased? Yes No

Explanation / Answer

The null hypothesis : H0 : =1950 pounds

ALternative Hypothesis : Ha : > 1950 pounds

As, standard deviation of popuation is given we will use Z - test here

sample size = 50

so first we will calculate standard error of the mean breaking strength = / sqrt (n) = 100/ sqrt (50) = 14.14

Test statistic

Z = (xbar - H )/ ( / sqrt (n) ) = (1963 - 1950)/ (100/ sqrt (50) ) = 13/ 14.14 = 0.92

Critical value at 0.1 level Z = 2.329

Here Z < Zcritical , so we cannot reject the null hypothesis and can discard the claim that mean breaking strength has increased.

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