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.
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.