A quality-assurance inspector periodically exam-ines the output of a machine to determine whether it is properly adjusted. When set properly, the machine pro-duces nails having a mean length of 2.000 inches, with a standard deviation of 0.070 inches. For a sample of 35 nails, the mean length is 2.025 inches. Using the 0.01 level of significance, examine the null hypothesis that the machine is adjusted properly. Determine and interpret the p-value for the test.

Step-by-step explanation:

From the given information;

The null hypothesis & alternative hypothesis:

The test statistics can be computed as:

The p-value = 2(Z > 2.11)  since this is a two-tailed test

The p-value = 2( 1 - Z < 2.11)

The p-value = 2 (1 -0.9826)

The p-value = 2 (0.0174)

The p-value = 0.0348

Decision Rule: To reject the  if the p-value is less than

Conclusion: We fail to reject and conclude that the population mean = 2, thus the machine is properly adjusted.

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