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

A random sample of 118 weights of teenagers is obtained and the last digit is recorded. The frequency of each digit is recorded in the following table. If people report their weight, they tend to round. Test the claim that the sample is from a population of weights in which the last digits did NOT occur with the same frequency.

**Last digit**

0

1

2

3

4

5

6

7

8

9

**Frequency**

20

15

9

8

12

15

6

13

8

12

[Hint: Be sure to watch the video at

**Week 5 Resources**on the “Chi-Square Goodness-of-Fit test (equal frequencies)” before attempting this problem. Instructions for performing this test in STATDISK can be found in the Statdisk User’s Manual.]

**Instructions**

Answers

Answers

Use the Chi-Square Goodness-of-Fit test to test the claim that the frequency is NOT the same. Use a significance level of 0.01.

Paste results here.

What are we trying to show here?

What is the p-value and what does it represent in the context of this problem?

State your conclusion. The conclusion statement has a prescribed format: it should include a comparison of the p-value and alpha, whether you reject or support the null hypothesis, and a verbal statement of which hypothesis is supported.

Repeat the above procedure deleting digits 0 and 5. Paste results here.

Do you get a different result? What do the results mean?

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

In the 2000 U.S. Census, the ages of individuals in a small town were found to be the following:

Less than 18

18-35

More than 35

20%

30%

50%

30%

50%

In 2010 the ages of 500 individuals from the same small town were sampled with the following results:

Less than 18

18-35

More than 35

111

165

224

165

224

Using an alpha of 0.05, test the claim that the population distribution of ages has changed in the last 10 years?

[Hint: Be sure to watch the video at

**Week 5 Resources**on the “Chi-Square Goodness-of-Fit test (unequal frequencies)” before attempting this problem. Instructions for performing this test in STATDISK can be found in the Statdisk User’s Manual.]

Instructions

Answers

Instructions

Answers

Complete the table as necessary. [Hint: You will need to compute the expected frequencies based on the previous poll results. Round to the nearest integer.]

**OBSERVED**

111

165

224

**EXPECTED**

Use the Chi-Square Goodness-of-Fit test for Unequal frequencies to see if there is a difference between the observed frequencies (2010) and the expected frequencies (2000). Use a significance level of 0.05.

Paste results here.

State the null and alternative hypotheses.

What conclusion would you reach, given the result of your Goodness-of-Fit test? Use the prescribed format of the conclusion statement.

Part III. Chi-Square Test of Independence

Part III. Chi-Square Test of Independence

An ice cream shop conducted a survey to see if there was a relationship between gender and ice cream flavor preference. Perform a Chi Square test of independence to determine whether there is an association between gender and preference for ice cream flavor.

Chocolate

Vanilla

Strawberry

Total

MenVanilla

Strawberry

Total

100

120

60

280

Women120

60

280

350

200

90

640

200

90

640

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

Answers

Just looking at the numbers in the table, what is your best guess about whether gender is related to ice cream flavor preference?

Compute a Chi-Square Test of Independence on this data using a 0.05 level of significance. Paste your results here.

What are the null and alternative hypotheses for this result?

What is the p-value for this result? What does this represent?

State your conclusion. Use the prescribed format of the conclusion statement.

Part IV. Apply this to your own situation

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**

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

OBSERVED

35

5

10

EXPECTED

25

10

15

Chocolate-Chip

Oatmeal-Raisin

Sugar-Cookie

OBSERVED

35

5

10

EXPECTED

25

10

15

Perform the test

Paste your STATDISK results here

State your conclusion

We have evidence to believe ….