EXPERIMENTAL DESIGN FOR INDUSTRIAL PROCESSES
IE 356 Module 2 Assignment

Completed Module 2 assignments can be handwritten or typed, and a pdf should be turned in through Canvas. Make sure you include your name on the submitted document. Adding other identifying information such as class and date is good practice.

Short answer (one or two sentence answers)

1. Consider the following example of a “simple” experiment presented in class. Do not complete the problem in the example.

Describe some possible experimental design and procedural issues that must be considered.

2. When conducting a statistical hypothesis test, why is it important which statement (about a particular parameter) becomes the null hypothesis? Use the problem in 1 as an example.

Specific procedures for some of the problems below were not covered in lecture. You will need to research the appropriate test procedure.

Problems

3. The diameters of steel shafts produced by a certain manufacturing process should have a mean diameter of 0.255 inches. The diameter is known to have a standard deviation of ? = 0.0001 inch. A random sample of 10 shafts has an average diameter of 0.2545 inches.

(a) Your interest is to test if the mean diameter is different than 0.255 inches. If it is not, time consuming expensive procedures will be required to adjust the process. Set up the appropriate hypotheses on the mean µ. Explain why you set up the hypothesis in your answer. (b) Test these hypotheses using ? = 0.05.

• What is the assumed mathematical model (model 1) for the diameter that you are assuming?

• Describe the test statistic, it’s sampling distribution, and why the sampling distribution is correct.

• What are your conclusions? (c) Find the P-value for this test.

4. A new filtering device is installed in a chemical unit. Before its installation, a random sample yielded the following information about the percentage of impurity: y 1 = 12.5, S1

2 =101.17, and n1 = 8.

After installation, a random sample yielded y 2 = 10.2, S2 2 = 94.73, n2 = 9.

(a) Can you concluded that the two variances are equal? Use ? = 0.05.

• What is the assumed mathematical model (model 1) for the percentage of impurity that you are assuming?

• Describe the test statistic utilized, it’s sampling distribution, and state the assumptions that leads to this sampling distribution.

• What are your conclusions?

(b) Has the filtering device reduced the percentage of impurity significantly? Use ? = 0.05.

• Describe the test statistic utilized, it’s sampling distribution, and state the assumptions that leads to this sampling distribution.

• What are your conclusions?