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Metalcraft Enterprises, Inc. manufactures precision tubular parts. One such part is a cylindrical tube with specified...

Metalcraft Enterprises, Inc. manufactures precision tubular parts. One such part is a cylindrical tube with specified diameter of 4 cm. Suppose a random sample of 16 of these tubes yields an average diameter of 3.985 cm with a standard deviation of 0.01 cm.

1.Based on the sample data, the 99% confidence interval estimate of the mean diameter, μ, of these tubes is:

2.

Which of the following statements is true if the 99% confidence interval is used to test H0: μ = 4 cm, Ha: μ ≠ 4 cm?

A)

There is not significant evidence that the mean diameter is not 4 cm.

B)

The P-value of the test is smaller than 0.01.

C)

The P-value of the test is larger than 0.01.

D)

The probability that the mean diameter is not 4 cm is 0.99.

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Answer #1

1. From the t table, for 15 degrees of freedom, the 99% confidence interval for the critical t values is:

Substituting t with the test statistic:

2. Since 4 does not lie in the 99% confidence interval, we reject the null hypothesis and conclude that the p-value of the test is less than 0.99. B is correct.

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