Statistics Question

An engineer responsible for a manufacturing process recorded the following data in inches about a process she is responsible for managing.

She is interested in seeing if the mean is different from the known mean of 15 inches. If she took this data randomly from 18 samples, at a significance level of 1% or 0.01, is there evidence to indicate that the mean from the sample is different from the known mean value of 15 inches?

Use the attached template to provide your results which includes the following sections.

1. State the Null and Alternative Hypothesis
2. State your assumptions and how you know they are reasonable.
3. Perform the hypothesis test or indicate why a hypothesis test could not be reasonably performed.
4. Describe your results and conclusions in narrative format

If it is assumed the population standard deviation is known and is equal to 1.8

1. Using your results, explain how you would know you were making a type I error
2. Using your results, explain how you would know you were making a type II error
3. If the true mean is, 14 inches, what is the power of this test?
4. If the true mean is 16 inches, what is the power of this test?