Part-1

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. Evaluate the probability (rounded to 2 decimal places) of committing a Type I error for this decision rule? Add all calculations in your submission report.

2. Prepare 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. Give specific advice for modifying the test to ensure both of the subsequent

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.

Part-2

1. Practice identification of proper analysis type (1-Sample Z, 1-Sample t, 2-Sample t, Paired t, etc).

2. Practice hypothesis testing.

3. Practice interpretation of statistical information.

Problem: The design of controls and instruments has a large effect on how easily people will use them. A student project investigated this effect by asking 25 right-handed students to turn a knob (with their right hands) that moved an indicator by screw action. There were two identical instruments, one with a right-hand thread (the knob turns clockwise) and the other with a left-hand thread (the knob turns counterclockwise). The times required (in seconds) were carefully recorded and are provided in the Excel file titled "Assignment #2 - Part III - Times."

Requirements: Again, use StatTools to prepare as much of the statistical information needed as possible.

1. Each of the 25 students used both instruments. Explain briefly how the experiment should be arranged and how randomization should be used.

2. The project hoped to show that right-handed people search right-hand threads easier to use. State the appropriate null and alternative hypotheses about the mean time required to complete the task.

3. Carry out a test of your hypotheses using a significance level of 0.05. Give the P-value and report your conclusion.

4. Evaluate the appropriate 95% confidence interval that could be used to test the hypotheses. Interpret the result.