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

In order to determine staffing levels, a hospital wants to determine if births occur with the same frequency on each day of the week. The table below lists the days of the week selected by a random sample of 100 births. Consider the claim that the days of the week have the same frequency of a birth occurring.

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

32

16

7

20

11

8

6

Instructions for performing this test in Stat Disk can be found in the Stat Disk User’s Manual under Goodness of Fit, Equal Frequencies.

Instructions

Answers

1. Use the Chi-Square Goodness-of-Fit test to see if there is a difference between the frequency of births and days of the week. Use a significance level of .01.

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? What do they 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 – 20% 18-35 – 30% and greater than 35 – 50%

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

Less than 18 – 121 people 18-35 – 288 people and greater than 35 – 91 people

Using an alpha of 0.05, would you conclude that the population distribution of ages has changed in the last 10 years? Instructions for performing this test in Stat Disk can be found in the Stat Disk User’s Manual under Goodness of Fit, Unequal Frequencies.

Instructions

Answers

6. Complete the table as necessary.

[Hint: You will need to compute the observed frequencies based on the percentages for the 500 samples. Round to the nearest integer.]

Less than 18

18-35

35-91

OBSERVED

121

288

91

EXPECTED

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 .05.

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

The following table is the result of a survey from a random sample of different crime victims.

Use the data to test the claim that the type of crime is independent of whether the criminal was a stranger. Use a significance level of 0.05.

Homicide

Robbery

Assault

Criminal was a stranger

12

379

727

Criminal was an acquaintance or relative

39

106

642

Hint: Instructions for performing this test in Stat Disk 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 type of crime and criminal being a stranger or not? Are they independent or is there a relationship?

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

12. What are the null and alternative hypothesis for this test?

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

OBSERVED

35

5

10

EXPECTED

25

10

15

Perform the test

Paste your STATDISK results here

State your conclusion

We have evidence to believe ….

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

In order to determine staffing levels, a hospital wants to determine if births occur with the same frequency on each day of the week. The table below lists the days of the week selected by a random sample of 100 births. Consider the claim that the days of the week have the same frequency of a birth occurring.

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

32

16

7

20

11

8

6

Instructions for performing this test in Stat Disk can be found in the Stat Disk User’s Manual under Goodness of Fit, Equal Frequencies.

Instructions

Answers

1. Use the Chi-Square Goodness-of-Fit test to see if there is a difference between the frequency of births and days of the week. Use a significance level of .01.

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? What do they 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 – 20% 18-35 – 30% and greater than 35 – 50%

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

Less than 18 – 121 people 18-35 – 288 people and greater than 35 – 91 people

Using an alpha of 0.05, would you conclude that the population distribution of ages has changed in the last 10 years? Instructions for performing this test in Stat Disk can be found in the Stat Disk User’s Manual under Goodness of Fit, Unequal Frequencies.

Instructions

Answers

6. Complete the table as necessary.

[Hint: You will need to compute the observed frequencies based on the percentages for the 500 samples. Round to the nearest integer.]

Less than 18

18-35

35-91

OBSERVED

121

288

91

EXPECTED

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 .05.

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

The following table is the result of a survey from a random sample of different crime victims.

Use the data to test the claim that the type of crime is independent of whether the criminal was a stranger. Use a significance level of 0.05.

Homicide

Robbery

Assault

Criminal was a stranger

12

379

727

Criminal was an acquaintance or relative

39

106

642

Hint: Instructions for performing this test in Stat Disk 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 type of crime and criminal being a stranger or not? Are they independent or is there a relationship?

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

12. What are the null and alternative hypothesis for this test?

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

OBSERVED

35

5

10

EXPECTED

25

10

15

Perform the test

Paste your STATDISK results here

State your conclusion

We have evidence to believe ….