Multiple Choice Practice for Inference for Quantitative Data: Slopes

Welcome to Unit 9 AP Statistics Multiple Choice Questions! Grab some paper and a pencil 📄 to record your answers as you go. You can see how you did on the Unit 9 Practice Questions Answers and Review sheet once you're done. Don't worry, we have tons of resources available if you get stumped 😕 on a question. And if solo study is not your thing, join a group in Hours!

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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

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

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)

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

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

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

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

A. Normal

B. Independence

C. Proportionality

D. Linear Relationship from Residuals

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

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

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%

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

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

A. Independence

B. Randomness

C. Normality

D. Proportionality

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

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

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

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