Question

The diameter of alloy rods produced on an extrusion machine are known to have a standard deviation of 0.0001 inches. A random sample of 25 rods have a mean diameter of 0.5046 inches. a) Test the hypothesis that the mean diameter is 0.5025 inches. Assume a 2-sided alternative and use α=.05. Be sure to identify the decision rule, the critical values. Draw pictures to visualize. b) Construct the 2-sided 95% confidence interval for this test with α=.05. c) What is the p value for this test? d) What is the power of the test if the true mean is 0.60? Please show this graphically

Answer 1

(a)

Conclusion: There is no evidence to conclude that the mean diameter is 0.5025 inches.

Following is the graph:

(b)

Conclusion: Since confidence interval does not contain 0.5025 so we reject the null hypothesis on the basis of confidence interval.

(c)

The p-value of the test is: 0.0000

(d)

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