AP Statistics



AP Statistics NAME _____________________________

Ch. 3 Review HOUR _______

1. Consider the following three scatterplots:

What is the relationship among [pic]and [pic], the correlations associated with the first, second, and third scatterplots, respectively?

A.) [pic]

B.) [pic]

C.) [pic]

D.) [pic]

E.) [pic]

2. A study found correlation r = 0.61 between the sex of a worker and his or her income. You conclude that

A.) Women earn more than men on the average.

B.) Women earn less than men on average.

C) An arithmetic mistake was made; this is not a possible value of r.

D. This is nonsense because r makes no sense here.

3. A copy machine dealer has data on the number x of copy machines at each of 89 customer locations and the number y of service calls in a month at each location. Summary calculations give [pic] = 8.4, sx = 2.1, [pic] = 14.2, sy = 3.8, and r = 0.86. What is the slope of the least squares regression line of number of service calls on number of copiers?

A.) 0.86

B.) 1.56

C.) 0.48

D.) None of these

E.) Can’t tell from the information given

4. In the setting of the previous problem, about what percent of the variation in the number of service calls is explained by the linear relation between number of service calls and number of machines?

A.) 86%

B.) 93%

C.) 74%

D.) None of these

E.) Can’t tell from the information given

5. Which of the following statements about the correlation coefficient are true?

I. The correlation coefficient and the slope of the regression line may have opposite signs.

II. A correlation of 1 indicates a perfect cause-and-effect relationship between the variables.

III. Correlations of +0.87 and -.87 indicate the same degree of clustering around the regression line.

A. I only

B. II only

C. III only

D. I and II

E. I, II, and III

6. Suppose we fit the least squares regression line to a set of data. What is true if a plot of the residuals shows a curved pattern?

A.) A straight line is not a good model for the data.

B.) The correlation must be 0.

C.) The correlation must be positive.

D.) Outliers must be present.

E.) The LSRL might or might not be a good model for the data, depending on the extent of

the curve.

7. A positive residual indicates that

A.) the regression line overpredicted the response variable.

B. The regression line underpredicted the response variable.

C. The regression line overpredicted the explanatory variable.

D. The regression line underpredicted the explanatory variable.

E. The predicted value of the variable is the same as the actual value of the variable.

8. A set of data relates the amount of annual salary raise and the performance rating. The least squares regression equation is [pic] = 1,400 + 2,000x where y is the estimated raise and x is the performance rating. Which of the following statements is not correct?

A.) For each increase of one point in performance rating, the raise will increase on average by $2,000.

B.) This equation produces predicted raises with an average error of 0.

C.) A rating of 0 will yield a predicted raise of $1,400.

D.) The correlation for the data is positive.

E.) All of the above are true.

9. Which of the following would not be a correct interpretation of a correlation of

r = –.30?

A.) The variables are inversely related.

B.) The coefficient of determination is 0.09.

C.) 30% of the variation between the variables is linear.

D.) There exists a weak relationship between the variables.

E.) All of the above statements are correct.

10. In the scatterplot in the previous question, if each x-value were decreased by one unit and the y-values remained the same, then the correlation r would

A.) Decrease by 1 unit

B.) Decease slightly

C.) Increase slightly

D.) Stay the same

E.) Can’t tell without knowing the data values

11. Suppose that the regression line for a set of data, y = 3 + bx, passes through the point (2,7). If [pic] and [pic]are the same means of the x- and y-values, respectively, then [pic]

A.) [pic] C.) [pic] E.) [pic]

B.) [pic] D.) [pic]

Part 2. Free Response

Questions 12-15 relate to the following.

Joey read in his biology book that fish activity increases with water temperature, and he decided to investigate this issue by conducting an experiment. On nine successive days, he measures fish activity and water temperature (in degrees Fahrenheit) in his aquarium. Larger values of his measure of fish activity denote more activity. The figure below presents the scatterplot of his data.

12. How would you describe the direction, form, and strength of the relationship from the scatterplot?

13. One of the following numbers is the correlation coefficient between fish activity and water temperature; circle the correct number:

–0.20 0.03 0.52 0.86

14. If temperature were measured in degrees Celsius instead of degrees Fahrenheit, how would the correlation change? Note that [pic].

15. Suppose a new point at (66, 500), that is, water temperature = 66(F and fish activity = 500, is added to the plot. What effect, if any, will this new point have on the correlation between fish activity and water temperature? Justify your answer.

For problems 16-21: The AP Statistics exam was first administered in May 1997 to the largest first-year group in any discipline in the AP program. Since that time, the number of students taking the exam has grown at an impressive rate. Here are the actual data. Begin by entering them into your calculator lists.

Number of

Year students 16.Use your calculator to construct a scatterplot of these data using 1997

1997 7,667 as Year 1, 1998 as Year 2, etc. Describe what you see.

1998 15,486

1999 25,240

2000 34,118

2001 40,259

2002 49,824

2003 58,230

2004 65,878

2005 76,786

17. Find the equation of the least-squares line on your calculator. Record the equation below. Be sure to define any variables used.

18. Interpret the slope of the least-squares line in context.

19. How many students would you predict took the AP Statistics exam in 2006? Show your method.

20. Construct a residual plot. Sketch it in the space below. Comment on what the residual plot tells you about the quality of your linear model.

21. Interpret the value of [pic] from your calculator in the context of this problem.

For problems 22-25: We often describe our emotional reaction to social rejection as “pain.” A clever study asked whether social rejection causes activity in areas of the brain that are known to be activated by physical pain. If it does, we really do experience social and physical pain in similar ways. Subjects were first included and then deliberately excluded from a social activity while changes in brain activity were measured. After each activity, the subjects filled out questionnaires that assessed how excluded they felt. The table below shows data for 13 subjects.

The explanatory variable is “social distress” measured by each subject’s questionnaire score after exclusion relative to the score after inclusion. (So values greater than 1 show the degree of distress caused by exclusion.) The response variable is change in activity in a region of the brain that is activated by physical pain.

22. Use your calculator to construct a scatterplot of

these data. Describe what you see.

23. Find the equation of the least-squares line on your calculator. Record the equation below. Be sure to define any variables used.

24. Show how to calculate the residual for the individual with social distress score 2.01.

25. What would you predict for the brain activity level for an individual with social distress 3.10?

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