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Unit 8

8.9 MC Answers and Review

8 min read•june 18, 2024

AP Statistics 📊

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Answers and Review for Multiple Choice Practice on Inference for Categorical Data: Chi-Square

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⛔STOP ⛔ Before you look at the answers make sure you gave this practice quiz a try so you can assess your understanding of the concepts covered in Unit 8. Click here for the practice questions: AP Statistics Unit 8 Multiple Choice Questions.

Facts about the test: The AP Statistics exam has 40 multiple choice questions and you will be given 1 hour 30 minutes to complete the section. That means it should take you around 11 minutes to complete 5 questions.

The following questions were not written by College Board and although they cover information outlined in the AP Statistics Course and Exam Description the formatting on the exam may be different.

1. An individual wants to run a chi-squared goodness of fit test to determine how students in three different education settings (lecture, group work, individual online work) performed on an exam in terms of pass/fail. How many degrees of freedom would you require for this GOF test?

A. 1

B. 2

C. 3

D. 5

Answer: The degree of freedom for a chi-squared goodness of fit test is one less than the number of categories. Since there are three categories here (lecture, group work and online), there would be 2 degrees of freedom.

📄 Study AP Statistics, Unit 8.3: Carrying Out a Chi Square Goodness of Fit Test

2. To verify large counts for any chi-squared test, we need to make sure our __________ counts are greater than ______.

A. Expected, 10

B. Observed, 5

C. Expected, 5

D. Observed, 10

Answer: We need at least 5 in each of our expected counts to run any of the three chi-squared tests in AP Statistics. This is similar to our normal check-in other units.

📄 Study AP Statistics, Unit 8.0: Unit 8 Overview

3. A chi-squared distribution only has ________ values.

A. Positive

B. Negative

C. Even

D. Decimal

Answer: The chi-squared distribution measures the distance from observed values and expected values. Distances are always positive, so our chi-squared distribution only contains positive values, regardless of our df.

📄 Study AP Statistics, Unit 8.0: Unit 8 Overview

4. What makes the skewness of a chi-squared distribution less pronounced?

A. Larger population

B. Larger sample size

C. Smaller confidence level

D. Larger degrees of freedom

Answer: As the degrees of freedom increase, our curve becomes more symmetric and less skewed. Our degrees of freedom with chi-squared is not directly related to the sample size, although it is likely the two may increase together.

📄 Study AP Statistics, Unit 8.3: Carrying Out a Chi Square Goodness of Fit Test

5. Which of the following is the correct alternate hypothesis for a chi-squared goodness of fit test?

A. At least one of the proportions in the null hypothesis is incorrect

B. There is an association between the two variables we are measuring.

C. There is not an association between the two variables we are measuring.

D. p=(given population proportion)

Answer: For a chi-squared GOF test, basically the alternate hypothesis is always the same. We are looking at one variable with multiple categories and our alternate hypothesis is that one of the null proportions is incorrect. Always be sure to include context though!

📄 Study AP Statistics, Unit 8.2: Setting Up a Chi Square Goodness of Fit Test

6. Which chi-squared test would be appropriate if we were to be measuring the difference in the proportion of MM colors, assuming that the proportion of all colors are equal?

A. Chi-Squared Test for Independence

B. Chi-Squared Test for Homogeneity

C. Chi-Squared Test for Association

D. Chi-Squared Goodness of Fit

Answer: Since we are only looking at one variable with multiple categories, a GOF test is appropriate here.

📄 Study AP Statistics, Unit 8.7: Skills Focus: Selecting an Appropriate Inference Procedure for Categorical Data

7. When running a chi-squared GOF test and obtaining a p-value of 0.02, what would our conclusion be after finishing the test?

A. Since our p-value is less than 0.05, we accept the alternate hypothesis. We have convincing evidence of the alternate hypothesis.

B. Since our p-value is less than 0.05, we reject the Ho. We have convincing evidence that at least one of the proportions in the Ho is incorrect.

C. Since our p-value is less than 0.05, we fail to reject the null hypothesis. We have convincing evidence that the null hypothesis proportions are true.

D. Since our p-value is less than 0.05, we accept the null hypothesis. There is no evidence that anything is different than what is stated in the null.

Answer: Since our p-value is really low, we know that it would be unusual for this to occur by random chance. Therefore, that gives us convincing evidence that at least one of the proportions listed in our null is incorrect.

📄 Study AP Statistics, Unit 8.3: Carrying Out a Chi Square Goodness of Fit Test

8. What do we assume when running any chi squared test?

A. The null hypothesis is false

B. The null hypothesis is true

C. The distribution is normal

D. The alternate hypothesis is true

Answer: We always assume that the null hypothesis is true. Once we know that the null hypothesis is true, then we can determine the chance that our outcome was due to random chance or to something being wrong with the null hypothesis.

📄 Study AP Statistics, Unit 8.2: Setting Up a Chi Square Goodness of Fit Test

9. When determining the expected counts from a two way table, which formula should we use?

A. Number of categories minus 1

B. (row total)(column total)/table total

C. row total minus 1

D. column total minus 1

Answer: To find the expected count for each cell in our two-way table (used for independence or homogeneity tests), we must multiply the row and column totals, then divide by the table total.

📄 Study AP Statistics, Unit 8.4: Expected Counts in Two Way Tables

10. Which of the following is an appropriate null hypothesis for a chi-squared test for independence?

A. There is no association between variable X and variable Y in our given population.

B. There is an association between the two variables we are measuring.

C. We have evidence of the two variables being connected

D. p1=0

Answer: For independence tests, our null hypothesis is always stating that there is no association between the two variables of interest in our population.

📄 Study AP Statistics, Unit 8.5: Setting Up a Chi-Square Test for Homogeneity or Independence

11. For a chi-squared test for homogeneity in a randomized experiment, which of the following is not necessary as a condition of inference?

A. All expected counts at least 5

B. Treatments randomly assigned

C. There are two samples that our data is drawn from.

D. Sample size at least 30

Answer: Our sample size does not need to be at least 30 for a chi-squared test for homogeneity. All of the other conditions are necessary (randomization, expected counts and to show it is a homogeneity test, two samples)

📄 Study AP Statistics, Unit 8.5: Setting Up a Chi-Square Test for Homogeneity or Independence

12. How do we determine the degrees of freedom for a chi square test with two variables (homogeneity or independence)?

A. Number of Rows minus 1

B. Number of columns minus 1

C. (number of rows-1)(number of columns-1)

D. Table total minus 1

Answer: The correct formula for degrees of freedom when there are two variables is taking the number of columns minus 1 and multiplying it by the number of rows minus 1.

📄 Study AP Statistics, Unit 8.6: Carrying Out a Chi-Square Test for Homogeneity or Independence

13. Mr. Barcel decides to perform a chi squared test to see if there is a significant difference in the flavor of Takis people prefer. Which test would be necessary to run here?

A. Chi Squared Goodness of Fit

B. Chi Squared Test for Independence

C. Chi Squared Test for Homogeneity

D. Chi Squared Test for Difference of Squares

Answer: Since we only have one variable (flavor), this would be a chi-squared GOF test

📄 Study AP Statistics, Unit 8.7: Skills Focus: Selecting an Appropriate Inference Procedure for Categorical Data

14. A random sample is taken between high school students on what their favorite type of cheese is and if they like cake or pie. Which chi-squared test would be appropriate here to determine if cheese and dessert preference are associated?

A. Chi Squared Goodness of Fit Test

B. Chi Squared Test for Homogeneity

C. Chi Squared Test for Difference of Squares

D. Chi Squared Test for Independence

Answer: Since we are only taking one sample, this would require a test for independence. We are checking to see if dessert and cheese preferences are associated with one population, not comparing two populations, so a test for homogeneity would not be appropriate.

📄 Study AP Statistics, Unit 8.7: Skills Focus: Selecting an Appropriate Inference Procedure for Categorical Data

15. A school counselor is interested if the preference between In N Out, Whataburger and McDonalds is different between two schools. To do so, she takes a random sample of 200 students from each school and asks their restaurant choice. What type of chi-squared test would be appropriate here?

A. Chi Squared Test for Independence

B. Chi Squared Goodness of Fit Test

C. Chi Squared Test for Homogeneity

D. Chi Squared Test for Difference of Squares

Answer: Since we have two samples here (two schools), this is a test for homogeneity. We are testing the difference in the distribution of restaurant preference between the two schools. We are looking at our two schools and if they are alike (homogenous) in their distribution of restaurant choice.

📄 Study AP Statistics, Unit 8.7: Skills Focus: Selecting an Appropriate Inference Procedure for Categorical Data

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