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AP Stats

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Unit 9

9.8 MC Answers and Review

7 min read•june 18, 2024

AP Statistics 📊

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Answers and Review for Multiple Choice Practice on Inference for Quantitative Data: Slopes

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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 9. Click here for the practice questions: AP Statistics Unit 9 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. A regression model is created to determine the correlation between the number of siblings and the size of the house. What type of hypothesis test would be appropriate to determine if the two items are correlated. Which type of test should we use to determine if it is correlated?

A. A linear regression z test for y-intercept

B. A linear regression t-test for slope

C. A T-test for Independence

D. A Chi-Square Test for Regression

Answer: Linear regression models always involve quantitative data. Therefore, we would run a t test and the slope is what determines if there is a linear correlation.

📄 Study AP Statistics, Unit 9.1: Introducing Statistics: Do Those Points Align?

2. A regression model is created to determine the correlation between the number of siblings and the size of the house. What type of hypothesis test would be appropriate to determine if the two items are correlated. What would be the appropriate hypotheses for running this model?

A. Ho: 𝜷 = 0; Ha: 𝜷 ≠ 0

B. Ho: 𝜷 = 1; Ha: 𝜷 ≠ 1

C. Ho: 𝝁 = 0; Ha: 𝝁 ≠ 0

D. Ho: 𝝁 = 1; Ha: 𝝁 ≠ 1

Answer: When testing for linear regression, we are generally testing against the null hypothesis that the slope is 0. We want to use 𝜷 to represent our slope, not 𝝁

📄 Study AP Statistics, Unit 9.4: Setting Up a Test for the Slope of a Regression Model

3. If I want to run a linear regression t-test to test between two variables, how would I find the degrees of freedom?

A. n

B. n-1

C. n-2

D. (n-1)(n-2)

Answer: When testing for correlation between two quantitative variables, you would use n-2 for your degrees of freedom for your t distribution.

📄 Study AP Statistics, Unit 9.5: Carrying Out a Test for the Slope of a Regression Model

4. From a computer output on a data set of 100 random individuals, we are given a slope of 1.43, a standard deviation of 3.67, a t-score of 11.3, and a p-value of 0.0001. What should we use as our critical value when constructing a 95% confidence interval for our slope?

A. 0.001

B. 1.43

C. 1.984

D. 11.3

Answer: When constructing a confidence interval, we are going to use a t score based on the 2.5% area to the left of our confidence zone, NOT the t score for OUR SAMPLE. That t score is used to show that it does fall in the rejection region since it is greater than 1.984. This would be calculated using a t score chart or invT function in the calculator.

📄 Study AP Statistics, Unit 9.5: Carrying Out a Test for the Slope of a Regression Model

5. From a computer output on a data set of 100 random individuals, we are given a slope of 1.43, a standard deviation of 3.67, a t-score of 11.3, and a p-value of 0.0001. How would we conclude this hypothesis test?

A. Since our t score is large, we do not have enough evidence that the two variables are correlated.

B. Since p<0.05, we conclude that there is a correlation between our two variables because we have significant evidence that the slope is not 0.

C. Since our slope is fairly close to 0, we do not have significant evidence that the true slope is anything different than 0.

D. We do not have enough information to tell

Answer: We always judge our hypothesis tests on our p-value, just like other hypothesis tests. Since it is small, we reject the null that the slope is 0 (aka not correlated).

📄 Study AP Statistics, Unit 9.5: Carrying Out a Test for the Slope of a Regression Model

6. Which p-value would likely match a correlation coefficient of 0.2?

A. 0.0006

B. 0.006

C. 0.06

D. 0.6

Answer: Since our r value was fairly low (not close to 1), that gives us an idea that the two variables are not very correlated. Therefore, our p value would not be particularly low and 0.6 makes the most sense.

📄 Study AP Statistics, Unit 9.5: Carrying Out a Test for the Slope of a Regression Model

7. Which condition is NOT necessary for linear regression inference?

A. Normal

B. Independence

C. Proportionality

D. Linear Relationship from Residuals

Answer: Proportionality is not one of the conditions necessary to run a linear regression t-test or interval.

📄 Study AP Statistics, Unit 9.2: Confidence Intervals for the Slope of a Regression Model

8. What from our residual plot shows us that the standard deviation of y changes with x?

A. Curve pattern

B. Linear Pattern

C. Fanning

D. All of the above

Answer: Anything showing some sort of pattern on our residual plot shows us that there is a correlation with our standard deviation of y as x varies. Any of these violate one of the conditions are is grounds to NOT continue performing our inference procedure.

📄 Study AP Statistics, Unit 9.2: Confidence Intervals for the Slope of a Regression Model

9. Which t score would likely be grounds for rejection of the null hypothesis for a linear regression t-test?

A. 0

B. 0.5

C. 0.9

D. 11.3

Answer: 11.3 is a high t score, meaning our sample would almost certainly fall inside the rejection region.

📄 Study AP Statistics, Unit 9.5: Carrying Out a Test for the Slope of a Regression Model

10. Which of the following is a correct interpretation of a p-value of 0.12?

A. Assuming that our null hypothesis is true, there is a 12% chance of getting a sample as extreme as ours by random chance alone.

B. Assuming that our null hypothesis is true, there is a 12% chance of rejecting the null.

C. There is a 12% chance of getting a slope of 0.

D. The probability of rejecting the null is 12%

Answer: The key part of a p-value interpretation is that it is under the assumption that the null hypothesis is true. It is the probability of obtaining a sample equal to, or more extreme, to the one we actually obtained randomly.

📄 Study AP Statistics, Unit 9.5: Carrying Out a Test for the Slope of a Regression Model

11. What distribution do we use for a linear regression t-test?

A. Z distribution

B. T distribution

C. Poisson Distribution

D. Chi-Square Distribution

Answer: In AP Statistics, we always use a t distribution for linear regression inference.

📄 Study AP Statistics, Unit 9.0: Unit 9 Overview

12. Which condition is the most important when running an inference procedure?

A. Independence

B. Randomness

C. Normality

D. Proportionality

Answer: Randomness is always the most important condition. There is no mathematical way to adjust for a lack of randomness. The other conditions that are necessary can be achieved by increasing sample size generally.

📄 Study AP Statistics, Unit 9.1: Introducing Statistics: Do Those Points Align?

13. How large does our sample size need to be for a skewed distribution to be approximately normal?

A. 5

B. 10

C. 20

D. 30

Answer: As with any quantitative data, the sample size needs to be at least 30 to satisfy the Central Limit Theorem.

📄 Study AP Statistics, Unit 9.2: Confidence Intervals for the Slope of a Regression Model

14. What aspect of a computer output serves as a point estimate for a confidence interval for a linear regression model?

A. Sample Slope

B. Sample y-intercept

C. S

D. R squared

Answer: Our sample slope serves as our point estimate since our confidence interval is an inference procedure used to estimate the slope of our population.

📄 Study AP Statistics, Unit 9.2: Confidence Intervals for the Slope of a Regression Model

15. Which procedure is often used to take a non-linear model and make it follow a linear trend?

A. Doubling the response variable values

B. Add 30 to each explanatory variable value

C. Square root all values of both variables

D. Natural log all values of the response variable

Answer: To transform data sets that are non-linear, we often take the natural log of all values of the response variable or square all values of the explanatory variable to attempt to create a more linear data set.

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