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AP Statistics: Unit – 9 – Inference for Quantitative Data (Slopes) Practice Test

September 19, 2020Brajendra Shrivastava

AP Statistics: Unit – 9 – Inference for Quantitative Data (Slopes) Practice Test

AP Statistics: Unit – 9 – Inference for Quantitative Data (Slopes) Practice Test

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Question 1 of 19

1. Question
In regression analysis, the y-variable should be the ______________ variable, and the x-variable should be the ______________ variable.
- Dependent, Independent
- Qualified, Unqualified
- Greater, Lesser
- First, Second
- Independent, Dependent
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Question 2 of 19

2. Question
You estimate a regression model with β = 3.4 and SE = .024, where β is the beta coefficient and SE is the standard error. Construct 95% confidence intervals for β.
- [3.4,3.45]
- [3.1,3.45]
- [3.35,3.45]
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Question 3 of 19

3. Question
Based on this confidence interval, what can you do with a hypothesis test at 5% significance level where H 0 : β 1 = 0 and H a : β 1 ≠ 0?
- Fail to reject the null hypothesis because this confidence interval does not include 0
- Reject the null hypothesis because this confidence interval does not include 1.
- Fail to reject the null hypothesis because this confidence interval does not include 1.
- Reject the null hypothesis because this confidence interval does not include 0.
- Not enough information to be able to decide.
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Question 4 of 19

4. Question
A statistician conducts a regression analysis and obtains a p-value of 0.1. It is more likely than not that there is a relationship between the variables in the study.
- Always True
- Always False
- Sometime False
- not enough data to determine
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Question 5 of 19

5. Question
Suppose you conduct a paired z-test to assess whether two group means significantly differ and find a z-score of 1.645. At what alpha level would this cause you to reject the null?
- 0.20
- 0.10
- 0.05
- 0.01
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Question 6 of 19

6. Question
A statistician conducts a regression analysis and obtains a p-value of 0.1. It is more likely than not that there is a relationship between the variables in the study.
- True
- False
- not enough data to determine
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Question 7 of 19

7. Question
For a data set, the least-squares regression line has a 95% confidence interval for the slope of (1.210, 1.318). Based on this confidence interval, what can you do with a hypothesis test at 5% significance level where H 0 : β 1 = 0 and H a : β 1 ≠ 0?
- Reject the null hypothesis because this confidence interval does not include 0.
- Not enough information to be able to decide.
- Fail to reject the null hypothesis because this confidence interval does not include 0.
- Reject the null hypothesis because this confidence interval does not include 1.
- Fail to reject the null hypothesis because this confidence interval does not include 1.
Correct

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Question 8 of 19

8. Question
Which of the following is an incorrect condition requirement for regression inference?
- A trend/pattern of some sort in the residual plot
- Response must vary normally about the regression line for any given value of x
- Ordered pairs must be independent of each other
- A linear relationship between x and y
- The standard deviation of the response must be constant
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Question 9 of 19

9. Question
Suppose you conduct a paired z-test to assess whether two group means significantly differ and find a z-score of 1.645. At what alpha level would this cause you to reject the null?
- 0.20
- 0.10
- 0.01
- 0.05
Correct

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Question 10 of 19

10. Question
Bob wants to statistically determine if the mean height of middle school boys is greater than the mean height of middle school girls. He wants to use a significance level of 0.05 What must be true for him to reject H o : μ boys = μ girls . σ is known.
- z > 1.64
- t > 1.96
- z > 1.96
- t > 1.64
- z > 1.64
Correct

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Question 11 of 19

11. Question
Which one of the following provides evidence that a condition for regression inference has been met?
- A Normal probability plot of the values for the explanatory variable shows a roughly linear form.
- A scatterplot of the residuals against the values of the explanatory variable displays a random scattering of points about the line residuals = 0.
- The data consists of at least 30 observations.
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Question 12 of 19

12. Question
Is there a relationship between reaction time and age? A statistics student measures the reaction time of 12 subjects by measuring how far a yardstick drops, in inches, before a subject catches it between his or her thumb and forefinger (a high number thus indicates a slow reaction time). The student plans to use linear regression to see if reaction time can be predicted by the age of the subject. Which one of the following is a correct set of hypotheses for testing the significance of this relationship?
- H 0 : β = 1, H a : β ≠ 1, where β = the true slope of the population regression line.
- H 0 : β = 0, H a : β ≠ 0, where β = the true slope of the population regression line
- H 0 : ρ = 1, H a : ρ < 1, where ρ = the true population correlation between age and reaction time.
- H 0 : ρ = 0, H a : ρ < 0, where ρ = the true population correlation between age and reaction time.
Correct

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Question 13 of 19

13. Question
Sarah runs an ice cream stand at a beach resort, and she is interested in predicting each day’s ice cream sales (in dollars) from the air temperature at 8:00 am (in degrees Fahrenheit). She randomly selects 12 days during the previous summer and calculates a least squares regression of sales on air temperature. A computer output of her regression is given below. Which one of the following is a correct interpretation of the number 1.646?
- For each 1° increase in air temperature, ice cream sales are predicted to increase, on average, by $1.65
- For samples of size 12, the typical deviation of a sample slope from the population (true) slope is estimated to be 1.646
- For this sample, the typical distance between an observed temperature and the mean temperature is 1.646
Correct

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Question 14 of 19

14. Question
Is there a relationship between reaction time and age? A statistics student measures the reaction time of 12 subjects by measuring how far a yardstick drops, in inches, before a subject catches it between his or her thumb and forefinger (a high number thus indicates a slow reaction time). The student plansto use linear regression to see if reaction time can be predicted by the age of the subject. Output from a computer regression analysis is given below.
- ^ y =2.580+ 0.30809 x
- ^ y =2.580 x +0.30809
- y =2. 716+0. 05051 x
Correct

Incorrect
Question 15 of 19

15. Question
mos collected data about population density (in thousand people per square n kilometer) and average rent for 1-bedroom apartments in a random sample of 25 cities. Here is computer output from a least-squares regression analysis on his sample: Assume that all conditions for inference have been met. Which of these is a 90%, percent confidence interval for the slope of the least squares regression line?
- 22.615 ± 1.714(4.179)
- 22.615 ± 1.645(4.179)
- 22.615 ± 1.319(4.179)
- 812 ± 1.645(109.8)
- 812 ± 1.319(109.8)
Correct

Incorrect
Question 16 of 19

16. Question
Cars lose value the farther they are driven. Heidi collected data about the mileage (in thousands of kilometers) and value (in thousands of dollars) of a randomsample of 11 cars of the same make and model. Here is computer output from a least-squares regression analysis on her sample:
- -0.246 ± 3.25(0.013)
- -0.246 ± 3.16(0.013)
- -0.246 ± 2.576(0.013)
Correct

Incorrect
Question 17 of 19

17. Question
Zoie took a random sample of 26 counties in her state and collected data regarding each county’s population and waste (in tons). Here is computer output on the sample data:Assume that all conditions for inference have been met. Which of these is an appropriate test statistic for testing the null hypothesis that the population slope in this setting is 0?
Correct

Incorrect
Question 18 of 19

18. Question
Leona collected data on the battery life (in hours) and price (in dollars) of a random sample of mobile phones. Here is computer output from a least-squares regression analysis on her sample: Assume that all conditions for inference have been met. Which of these is an appropriate test statistic for testing the null hypothesis that the population slope in this setting is 0?
Correct

Incorrect
Question 19 of 19

19. Question
Hashem obtained a random sample of students and noticed a positive linear relationship between their ages and their backpack weights. A 95%, percent confidence interval for the slope of the regression line was 0.39 ± 0.23. Hashem wants to use this interval to test H 0 : β = 0, H a : β ≠ 0 at the α = 0.05 level of significance. Assume that all conditions for inference have been met. Which of these is the most appropriate conclusion for this population of students?
- Reject H 0 . Hashem can't conclude a linear relationship between age and backpack weight.
- Fail to reject H 0 . Hashem can't conclude a linear relationship between age and backpack weight.
- Reject H 0 . This suggests a linear relationship between age and backpack weight.
- Fail to reject H 0 . This suggests a linear relationship between age and backpack weight.
Correct

Incorrect

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