Learning Objective: Reinforce understanding of Power, β, and α.
Problem: A packing process is designed to fill steel drums with 400 pounds of a chemical. To determine whether or not the process is working properly, a significance test has been designed. The null and alternative hypotheses are:
H0: μ = 400
Ha: μ ≠ 400
where μ is the average amount of chemical filled in the drums. It is decided to reject H0 if the average weight of a random sample of 36 drums is less than 390 pounds or if the average weight of a random sample of 36 drums is greater than 410 pounds. Assume that the population standard deviation is equal to 42, and that the drum fill weights are normally distributed.
Requirements:
1. Determine the probability (rounded to 2 decimal places) of committing a Type I error for this decision rule? Include all calculations in your submission report.
2. Create a power curve for this decision rule using the following alternate values for μ:
375, 380, 385, 390, 395, 400, 405, 410, 415, 420, 425. Include any manual calculations you do in the assignment submission.
3. Provide specific advice for modifying the test to ensure both of the following
a. a maximum probability of Type I error equal to 0.05
b. a maximum probability of Type II error equal to 0.15 when the mean amount of chemical in the drums is actually 410 pounds.