#### TESTS Of GOODNESS Of FIT & INDEPENDENCE

### The Big Idea

We will use Statgraphics to answer a question of real interest – what does a survey tell us about customers’ preferences?- via chi squared and proportion test tools. You will use both a difference of two proportions and a chi squared test of independence to look for evidence that gender affects answer to the “price” question. You will use a chi squared test of independence to look for evidence that zip code affects answers to the “price” question.

#### 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 include a copy of The Stat Advisor**- Be sure to state your conclusions in your words—don’t just copy the StatGraphics conclusions. We want to be independent thinkers, right?

### Project Assignment Details

#### Step 1: Assignment Data

Download the data file __Project Assignment Data__ (this can also be found in the files menu). You’ll need to open statgraphics, then open by selecting File->Open->Open Data Source, choose “External Data File”, then browsing for your excel file.

#### Step 2: Project Report

As you work through the assignment, write your report using either the provided __Project Assignment 1 Template__ or create your own document from scratch.

**Page 1**

Make a cover page, including your name, the date, instructor’s name, and “Project #1: Tests of Goodness of Fit & Independence”.

**Page 2**

Describe the data. Where does it come from? How is it formatted? Answer this in your own words, as clearly and succinctly as possible. You will want to review and reference both the __survey review example__ and the excel file.

**Page 3**

Does a person’s gender affect whether or not people think their TV service is priced reasonably? See if Price (treated as a category with seven levels) depends upon gender.

*Hint: In Statgraphics choose Describe -> Categorical -> Crosstab. Make sure you check the box for “test of independence”. Those percentages can be distracting, so you might want to right click on the table, select “Pane Options” and uncheck the percentages box. ***Then interpret the resulting p-value in your own words, in terms of the original question of interest!**

Now evaluate the same question in another way, using a difference of two proportions.

With regard to survey question #1: Is the proportion of men who agree that the service is reasonably priced really different than that of the proportion of women who agree so?

To answer this question, perform a hypothesis test on the difference between the proportion of men who answered 5, 6, or 7 vs. the proportion of women who answered 5, 6, or 7: This will probably be easiest if you use the crosstabulation table you created above.

Is there a difference between the genders in their agreement categories (test in this order: pmen – pwomen )?

State your conclusion, in your own words. Use the **p-value approach** and test against and α = 0.05

*Hint: Statgraphics can perform a test of the difference of two proportions. You may either share your statgraphics output or the equivalent hand calculations. To use statgraphics choose Compare -> Two Samples -> Hypothesis Tests. From there you will have to enter in the sample size for each group and the proportion of customers in each group that rated price as 5, 6, or 7. ***Then interpret the resulting p-value in your own words, in terms of the original question of interest!**

Now answer the question: **If these two results are identical, why is this so? If these two results are not identical, explain why and what this means for our question of interest: Does gender affect answer to the “price” question?**

**Page 4**

Does Zip code affect the answer to the price question? Again treat price as a categorical answer and use a chi-squared test of independence.

*Hint: In Statgraphics choose Describe -> Categorical -> Crosstab. Make sure you check the box for “test of independence”.* **Then interpret the resulting p-value in your own words, in terms of the original question of interest!**

Reflection Question: **Was it reasonable to treat answers to the price question as a categorical variable? Why or why not? What have you learned from this exercise that will be of value to you in future statistical work?**