I'm so confused.

Lexico specializes in the manufacture of coated cables. Quality is a high priority at Lexico, and to ensure that products they supply to customers meet specifications and are defect free, Lexico relies heavily on quality assurance sampling. Suppose for a particular cable the specification is that the amount of weight required to break it is more than 1,000 pounds. Suppose that in quality checks, 9 segments of the cable from each batch are tested to determine the applied weight at which each cable breaks. The sample average breaking weight is then used to determine if the average weight required to break the cable for the whole batch is in excess of 1,000 pounds.

The hypotheses: H0: μ ≤ 1,000 Ha: μ > 1,000

The mean weight required to break the cable in the whole batch is μ. Further suppose that an observed sample average is statistically significant if it is greater than 1010 pounds. Assume that the standard deviation in breaking weights is equal to 27 pounds, and that the breaking weights follow a normal probability distribution.

1. Determine the maximum probability (rounded to 2 decimal places) of committing a Type I error for the decision rule being utilized in the quality assurance check?

2. Create a power curve for this decision rule using the following alternate values for μ: 990, 995, 1000, 1005, 1010, 1015, 1020. You MUST use Excel, Minitab, or other software to create the graph of the power curve.

3. Provide specific advice for modifying the test to simultaneously ensure both of the following requirements.

a. a maximum probability of Type I error equal to 0.01

b. a maximum probability of Type II error equal to 0.05 when the mean breaking weight is

actually 1020 pounds.

4. Provide insight(s) into how it is possible to have such low error probabilities for both the type I and type II error with what might seem like a small change in the sample size.