ANOVA Test of Multiple Mean

 

SCENARIO: A cable company is interested in learning more about customer satisfaction. The company sent a survey (in paper format, but with a wax seal on the envelope – it looked very classy) to a randomly selected group of client households, and received 97 valid responses. The questions included the following:

Q1. My cable TV service is priced reasonably.
Strongly Disagree	1	2	3	4	5	6	7	Strongly Agree

 

Q3. The variety of programs is
Very Poor	1	2	3	4	5	6	7	Really Great

 

Q10. Gender:	0: Male				1: Female
Q11. Zip code:	97201		97219				97221
Q12. Age group:	18 – 24	25 – 34		35 – 49		50 – 60		61 and over

The Big Idea

We will use Statgraphics to answer a question of real interest.

Project Rules

Format

• Your report must be word processed and saved as a .pdf, .doc, or .docx.
• The report should contain 3-4 pages. Page #1 is the cover sheet. It should include your name, the instructor’s name, the date, and “Project #2: ANOVA Test of Multiple Means”.
• For manual calculations, you may write them and include a scan, but be neat and concise.
• Do not repeat the question or instructions; just follow the order given.
• Supporting graphs and tables should be imbedded within the report; not in an appendix.
• You may use the example template or create your own “from scratch”. If you use the template be sure to erase the “hint text” (often in brackets [ ]) before finishing.

StatGraphics

• StatGraphics is required for this project. Use it as much as possible. StatGraphics assistance is provided within the assignment.
• Be concise and include only essential Statgraphics results to support your argument.
• Show all required calculations—manual calcs and StatGraphics calcs
• Do not include extraneous StatGraphics output; i.e., do not include any StatGraphics printout that you do not know how to interpret.
• Do not print a copy of The Stat Advisor
• Be sure to state your conclusions in your words—don’t just copy the StatGraphics conclusions.

Grade-Related Issues

• You must upload an electronic copy to the course website before the deadline- please allow time for inevitable computer headaches!
• This assignment’s deadline is:
• Late projects are not accepted—zero points.
• Be sure you have reviewed the entire document and understand the contents.
• SUBMIT YOUR OWN WORK. You are not allowed to work together in any way.

Grading Rubric

Points	Basis for Grade
6	Clarity, formatting, legibility
6	Price vs. Gender
6	Reflection Question 1
6	Variety vs. Zip Code
6	Reflection Question 2

 

1. Use StatGraphics to generate side-by-side boxplots for Male and Female responses to the “Price” question.
2. Generate an ANOVA report for the difference between these categories.
3. Conduct (by hand or using statgraphics) a t test of the difference of these two means. How does this p-value compare to the p-value from your ANOVA table?
4. Based on the boxplot; discuss the results; i.e., write a report (in your words, 25-50 words) –> Compare the table data. What does the “data tell you” about the difference between the genders on this question?

Reflection Question #1: on the previous project we used a chi-squared test to address this same data. What was the difference between these two approaches? Which approach is better, and why?

Page 3

Does the answer to the “Variety” question vary by zip code? [Use StatGraphics output. Cut & paste directly but only the requested information.

Hint: Same as for page 2, and be sure “ANOVA Table” is checked as an option. For Reference: See statgraphics “how-to” videos

1. Use StatGraphics and generate and print an analysis of variance (ANOVA) table for the ”Variety” question with the three Zip Code levels “treatments”. Based on the table results, conduct a test of hypothesis about the equality of the true mean satisfaction with the variety of shows for all three treatment means in your words –> Use the p-value Method, α=0.05 and do the following, all within the context of the problem (i.e., in your words):
   1. state the hypotheses;
   2. state the p-value; and

• state the conclusion (use the scenario information to state this, and use your rejection criteria)

2. Use StatGraphics and generate and print an analysis of variance (ANOVA) table for the ”Variety” question with the Age levels “treatments”. Based on the table results, conduct a test of hypothesis about the equality of the true mean satisfaction with variety across age levels: in your words –> Use the p-value method, α=0.10 and do the following, all within the context of the problem (i.e., in your words):
   1. state the hypotheses;
   2. state the p-value; and

• state the conclusion (use the scenario information to state this, and use your rejection criteria).

Reflection Question #2: Does it seem reasonable to you that we use two different levels of significance for these two questions? If so, why? If not, why not? In either case, when does it seem reasonable to you to use a different value than 0.05 for alpha?