Reference no: EM133148260

Instructions concerning Problems 1 - 3:

1. Identify the design. "Identity design" means identify the number of design factors and the randomization procedure used. For example, one-factor factorial experiment for CRD, split-plot design with one (two, three) factors, nested design, and etc.

2. Determine whether it is a fixed-effect, random-effect, or mixed-effect model.

3. Give a model equation and describe the model parameters in the context of the problem.

4. State the model assumptions.

5. State the experimental hypotheses and describe them in the context of the problem.

Problem 1:

A quality control engineer is considering implementing a workshop to instruct workers on the principles of total quality management (TQM). The engineer has designed a study to evaluate which of the four workshops (Wsh#1, Wsh#2, Wsh#3, Wsh#4) used by other corporations would be the most effective. The response variable will be the increase in productivity of a worker after attending the assigned workshop. Since the effectiveness of the workshop may depend on the worker's preconceived attitude concerning TQM, the workers are given an examination to determine their attitude prior to taking the workshop. Their attitudes are classified into five groups: positive, negative, neutral, proactive, passive. Each attitude group contains four workers who are randomly assigned to one of the workshops. For each participant, the increases in productivity after taking the assigned workshop is recorded.

Problem 2:
A study was designed to evaluate the effectiveness of the new treatment strategies to reduce the systolic blood pressure of patients determined to have high blood pressure. Three drugs were selected for evaluation (D1, D2, 1D3). There are also three nondrug treatments for reducing blood pressure which are controlled diet, exercise programs, biofeedback (or simply Diet, Exercise, Biofeedback). The age of the patient usually hinders the effectiveness of any treatment. Thus, patients with high blood pressure were divided into two age groups (Al, A2). A sample of 54 patients from each age group was randomly selected and assigned to a combination of one of the three drugs and one of the three nondrug treatments. After participating in the program for two months, the reduction in systolic blood pressure was recorded for each patient.

Problem 3:

A major food distributor wanted to evaluate three different types of promotions on sales of its microwave pizza. The company's marketing department identified three types of promotions for use in grocery stores.

Promotion 1. Samples of product given to customers in the store with no additional sheii space in the store.
Promotion 2. Additional shell space in the standard locations in the store.
Promotion 3. Special display shelves at the end of aisle in addition to standard shelf space in the

Five stores were randomly assigned to each of the three promotions. The number of sales (y) of the product during the promotion period is recorded. Because the stores have different types of customers - that is, customers more or less inclined to pinchase the product - the number of sales of the product in the period preceding the promotion was recorded at each of the stores. It mny be crucial to control this factor because the stores with the highest sales in the months prior to the promotion would be expected to have higher sales during the promotion. This could mask the effects of any promotional differences.

Problem 4:
The goal of the study was to determine the effects of five different fertilizers (Fer1, Fer2, Fer3, Fer4, Fer5) on yields of wheat (in pounds).
• The experiment was conducted on five local forms (Fa1, Fa2, Fa3, Fa4, Fa5).

• Five plots were selected based on their soil fertility at each farm with the most fertile plots designated us l and the least fertile plots desigriated as 5.

a. The reseamhers ure facing a problem. The need to apply the fertilizers (randomly) to the plots. What is the best randomization technique that you would recommend in this case and why?

b. Based on the technique thnt you suggested in part a, assign the fertilizers to the plots (fill in the cells of the table with a fertilizer). Explain how you obtain the assignment.

Note: Need Problem 3, 4.