HW 2 JMP
Module 2 Homework Assignment.
Please analyze the following problems in JMP and answer the questions below.
1. Given a recent outbreak of illness caused by E.coli bacteria, the mayor of a large city is concerned that some of his restaurant inspectors are not consistent with their evaluations of a restaurant cleanliness. In order to investigate this possibility, the mayor has five restaurant inspectors grade (scale of 0 to 100) the cleanliness of three restaurants.
|
Inspector |
Restaurant |
||
|
|
1 |
2 |
3 |
|
1 |
72 |
54 |
84 |
|
2 |
68 |
55 |
85 |
|
3 |
73 |
59 |
80 |
|
4 |
69 |
60 |
82 |
|
5 |
75 |
56 |
84 |
a. Perform some descriptive statistics on the data. What are the average cleanliness scores for the 3 restaurants and the average cleanliness score given by the 5 inspectors?
b. State the model and all of the appropriate hypotheses being tested for this Two-way ANOVA problem
c. Run a two-way ANOVA analysis and draw your conclusions. What is your conclusion about the average cleanliness score between the three restaurants? What is your conclusion about the effect of the 5 inspectors on the cleanliness score? Is there any interaction between the Factors?
d. Check the residual plots and comment on the adequacy of the model.
2. Let us suppose that the Human Resources Department of a company desires to know if occupational stress varies according to age and gender. The variable of interest is therefore occupational stress as measured by a scale (higher scores = more stress). There are two factors being studied - age and gender. The employees have been classified into three age groups: age less than 40, age 40 to 55, and age above 55. In addition employees have been labeled into gender classification: male or female. Scores on occupational stress from employee(s) were obtained.
|
GENDER |
AGE |
OCCUPATIONAL STRESS |
|
Male |
Less than 40 |
68 |
|
Male |
40 to 55 |
70 |
|
Male |
Above 55 |
44 |
|
Male |
Less than 40 |
54 |
|
Male |
40 to 55 |
66 |
|
Male |
Above 55 |
52 |
|
Male |
Less than 40 |
78 |
|
Male |
40 to 55 |
62 |
|
Male |
Above 55 |
66 |
|
Male |
Less than 40 |
80 |
|
Male |
40 to 55 |
56 |
|
Male |
Above 55 |
42 |
|
Male |
Less than 40 |
58 |
|
Male |
40 to 55 |
72 |
|
Male |
Above 55 |
72 |
|
Female |
Less than 40 |
54 |
|
Female |
40 to 55 |
60 |
|
Female |
Above 55 |
44 |
|
Female |
Less than 40 |
42 |
|
Female |
40 to 55 |
42 |
|
Female |
Above 55 |
38 |
|
Female |
Less than 40 |
66 |
|
Female |
40 to 55 |
48 |
|
Female |
Above 55 |
42 |
|
Female |
Less than 40 |
58 |
|
Female |
40 to 55 |
59 |
|
Female |
Above 55 |
52 |
|
Female |
Less than 40 |
66 |
|
Female |
40 to 55 |
65 |
|
Female |
Above 55 |
50 |
a. Perform some descriptive statistics on the data. What are the average stress score and standard deviations for the different grouping variables? Create a graph that summarizes the data (boxplot, bar graph or something similar).
b. State the model and all of the appropriate hypotheses being tested for this Two-way ANOVA problem
c. Run a two-way ANOVA, with Age, Gender, and the interaction term. Is there an interaction between Age range and Gender of employee? If so, interpret the interaction through an LSmeans plot and multiple comparison confidence intervals. If no interaction is present, draw your conclusion about occupational stress between Ages and your conclusion about the effect of Gender on occupuational stress.
d. Calculate the average stress prediction for the following categories of employees
i. A 65 year old female employee
ii. A 29 year old male employee
iii. A 47 year old female employee