Week 5 Project – STAT 3001

Week 5 Project – STAT 3001

Student Name: <Type your name here>

Date: <Enter the date on which you began working on this assignment.>

This assignment is worth a total of 60 points.

Part I. Chi-Square Goodness of Fit Test (equal frequencies)

The table below lists the days of the week selected by a random sample of 1005 subjects who were asked to identify the best day of the week for family activities. Consider the claim that the days of the week have the same chance of being chosen.

Sunday Monday Tuesday Wednesday Thursday Friday Saturday
523 20 9 19 11 41 382

Instructions for performing this test in STATDISK can be found in the Statdisk User’s Manual.]

Instructions Answers
1. Use the Chi-Square Goodness-of-Fit test to see if there is a difference between the choices for best day for family activities. Use a significance level of .05.

Paste results here.

2. What are we trying to show here?
3. What is the p-value and what does it represent in the context of this problem?
4. State in your own words what the results of this Goodness-of-fit test tells us.
5. Repeat the above procedure using only the weekdays Paste results here. Did you get different results?

Part II. Chi-Square Goodness of Fit Test (unequal frequencies)

A personnel director claims that the distribution of the reasons withers leave their job is different from the distribution: 41% limited advancement; 25% lack of recognition; 15% low salary/benefits; unhappy with management 10%; 9% bored. You randomly select 200 workers who recently left their jobs and record each worker’s reasons for doing so. The table below show the results. At the 0.01 level of significance, test the personnel director’s claim.

Survey Results
Response Frequency
Limited advancement 78
Lack of recognition 52
Low salary/benefits 30
Unhappy with management 25
Bored 15
Instructions Answers
6. Complete the table as necessary.

[Hint: You will need to compute the expected frequencies based on the percentages for the 200 customers. Round to the nearest integer.]

advancement recognition salary management bored
1. OBSERVED 78 52 30 25 15
7. Use the Chi-Square Goodness-of-Fit test for Unequal frequencies to see if there is a difference between the observed frequencies and the expected frequencies Use a significance level of 0.01.

Paste results here.

8. State the null and alternative hypothesis.
9. What conclusion would you reach, given the result of your Goodness-of-Fit test? [State in your own words following the guidelines for a conclusion statement learned last week.]

Part III. Chi-Square Test of Independence

You work for a college’s continuing education department and want to determine whether the reasons given by workers for continuing their education are related to the job type. IN your study, you randomly collect the data shown in the contingency table. At the 0.01 level of significance, can you conclude that the reason and the type of job are dependent?

The following data was collected related to method of treatment and success/failure

Reason for continuing education
Type of worker Professional Personal Professional & personal
Technical 30 36 41
Other 47 25 30

Hint: Instructions for performing this test in STATDISK can be found in the Stat Disk User’s Manual under the heading Chi Square Test of Independence (Contingency Tables).

Instructions Answers
10. Just looking at the numbers in the table, what is your best guess about the relationship between reason for continuing education and job type? Are they independent or dependent?
11. Compute a Chi-Square Test of Independence on this data using a 0.01 level of significance. Paste your results here.
12. What is the null and alternative hypothesis for this result?
13. What is the p-value for this result? What does this represent?
14. State your conclusion related to the context of this problem.

Part IV. Apply this to your own situation

Using one of the above statistical tests, compose and SOLVE an actual problem from the context of your own personal or professional life. You will need to make up some data and describe which test you will use to analyze the situation. Here’s an example:

Example: Do not use this problem!!
State the problem that you are analyzing. Last year, I asked the kids in my neighborhood what kind of cookies they preferred. 50% said chocolate-chip, 20% said oatmeal-raisin, and 30% said sugar cookie. I want to see if this has changed.
Make up some data for the new situation. I asked 50 neighborhood kids what kind of cookie they preferred now and here’s what they said:

· 35 said chocolate-chip

· 5 said oatmeal-raisin

· 10 said sugar-cookie

Determine which type of Chi-Square test you will perform. Since these are unequal frequencies, I will perform a Chi-Square Goodness-of-Fit Test (Unequal Frequencies).
Specify your null and alternative hypotheses. H0: There is no difference this year in the preferences of cookies within the neighborhood kids.

H1: Things have changed.

Setup the test Chocolate-Chip Oatmeal-Raisin Sugar-Cookie
3. OBSERVED 35 5 10
4. EXPECTED 25 10 15
Perform the test Paste your STATDISK results here
State your conclusion We have evidence to believe ….

Submit your final draft of your Word file by going to Week 5, Project, and follow the directions under Week 5 Assignment 2. Please use the naming convention “WK5Assgn2+first initial+last name” as the Submission Title.

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