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, µ, of 1875 pounds, and a standard deviation of 60 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 44 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1879 pounds. Assume that the population is normally distributed. 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.

• The null hypothesis Ho:

• The alternative hypothesis H1:

• The type of test statistic:

• The value of the test statistic:

• The critical value at the 0.01 level of significance:

• Can we support the claim that the mean breaking strength has increased?

Explanation / Answer

• The null hypothesis Ho: MIU = 1875

• The alternative hypothesis H1: MIU > 1875

• The type of test statistic: Z test

• The value of the test statistic: Z = ( 1879-1875) / (60 / srqt44 ) = 0.44

• The critical value at the 0.01 level of significance: 2.32

• Can we support the claim that the mean breaking strength has increased?

No because Z < critical value we fail to reject Ho

there is no evidence to support the claim

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