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Test 4D
AP Statistics
Name:
Directions: Do all of your work on these sheets. Part 1: Multiple Choice. Circle the letter corresponding to the best answer. 1. A biologist plotted data from an experiment. He was interested in obtaining a least squares regression line. However, the data did not appear to be linear, so a variety of transformations were applied. Based on the following residual plots, which transformation was most effective in linearizing the data?
(a)
(b)
(c)
(d)
(e)
Chapter 4
1
Test 4D
A review of voter registration records in a small town yielded the following table of the number of males and females ed as Democrat, Republican, or some other affiliation. Democrat Republican Other
Male Female 300 600 500 300 200 100
2. The proportion of males that are ed as Democrats is (a) 300. (b) 0.33. (c) 0.30.
(d) 0.15.
(e) 0.375.
3. The proportion of all voters who are male and ed as Democrats is (a) 300. (b) 0.33. (c) 0.30. (d) 0.15.
(e) 0.375.
4. Recent data show that states that spend an above-average amount of money X per pupil in high school tend to have below-average mean Verbal SAT scores Y of all students taking the SAT in the state. In other words, there is a negative association between X and Y. This is particularly true in states that have a large percent of all high school students taking the exam. Such states also tend to have larger populations. The most plausible explanation for this association is (a) X causes Y. Overspending generally leads to extra, unnecessary programs, diverting attention from basic subjects. Inadequate training in these subjects generally leads to lower SAT scores. (b) Y causes X. Low SAT scores creates concerns about the quality of education. This inevitably leads to additional spending to help solve the problem. (c) changes in X and Y are due to a common response to other variables. If a higher percent of students take the exam, the average score will be lower. Also, states with larger populations have large urban areas where the cost of living is higher and more money is needed for expenses. (d) changes in X and Y are due to confounding with a third variable. As an example, states in which more money is spent on education tend to be those states with more students living in poverty. As a result, it’s the students’ living conditions that lead to lower SAT Verbal scores, and not the amount spent per pupil. (e) the association between X and Y is purely coincidental. 5. The following two-way table categorizes suicides committed in a particular year by the sex of the victim and the method used. Method Firearms Poison Hanging Other
Male 13,959 3,148 3,222 1,457
Female 2,641 2,469 709 690
Which of the following statements is consistent with the table? (a) There is absolutely no evidence of a relation between the sex of the victim and the method of suicide used. (b) More women commit suicide than men. (c) Men display a greater tendency to use firearms to commit suicide than do women. (d) The correlation between method of suicide and sex of the victim is clearly positive. (e) Females prefer poison over any other method of committing suicide.
Chapter 4
2
Test 4D
Part 2: Free Response Answer completely, but be concise. Show your thought process clearly. 6. The table below presents Census Bureau data on the years of school completed by Americans of different ages. Many people under 25 years of age have not completed their education, so they are left out of the table. The entries in the table are the counts of persons in each age-by-education class. Although both age and education in this table are categorical variables, both have a natural order from least to most. The order of the rows and columns in the table reflects the order of the categories. Years of school completed, by age, 2000 (thousands of persons) Age group Education 25 to 34 35 to 54 55+ Did not complete high school 4,474 9,155 14,224 Completed high school 11,546 26,481 20,060 1 to 3 years of college 10,700 22,618 11,127 4 or more years of college 11,066 23,183 10,596 Total 37,786 81,435 56,008
Total 27,853 58,087 44,445 44,845 175,230
(a) Calculate the marginal distribution of education level.
(b) Calculate the conditional distribution of age group, given “did not complete high school.”
(c) Make a bar graph to display the conditional distribution from (b). Be sure to label your graph.
(d) Describe what the graph in (c) tells you.
Chapter 4
3
Test 4D
7. An experiment was conducted to determine the effect of practice time (in seconds) on the percent of unfamiliar words recalled. Here is a Fathom scatterplot of the results with a least-squares regression line superimposed. (a) Sketch a residual plot below.
(b) Does a linear model fit the data well? Justify your answer.
We used Fathom to transform the original data in hopes of achieving linearity. The screen shots below show the results of two different transformations.
(c) Would an exponential model or a power model fit the original data better? Justify your answer.
(d) Use the model you chose in (c) to predict word recall for 25 seconds of practice. Show your method.
Chapter 4
4
Test 4D
8. From tax records, it is relatively easy to determine the amount of liquor consumed per person and the number of cigarettes consumed per person for each of the 10 provinces of Canada. These are plotted on a scatterplot and a high positive correlation is found. Is the association between these two variables most likely due to causation, confounding, or common response? Justify your answer.
9. A company decided to expand, so it opened a new factory with 455 available jobs. The following tables summarize the hiring decisions made by the company. Workers Managers Male Female Male Female Applied 400 100 Applied 200 200 Hired 300 85 Hired 30 40 (a) Calculate the percent of male and female workers that are hired. Then do likewise for male and female managers.
(b) Use the tables above to create a two-way table that shows the relationship between gender and hiring decision.
(c) Calculate the percent of male and female applicants that were hired.
(d) Explain your findings in (a) and (c).
I pledge that I have neither given nor received aid on this test._____________________________ Chapter 4
5
Test 4D
AP Statistics
Name:
Directions: Do all of your work on these sheets. Part 1: Multiple Choice. Circle the letter corresponding to the best answer. 1. A biologist plotted data from an experiment. He was interested in obtaining a least squares regression line. However, the data did not appear to be linear, so a variety of transformations were applied. Based on the following residual plots, which transformation was most effective in linearizing the data?
(a)
(b)
(c)
(d)
(e)
Chapter 4
1
Test 4D
A review of voter registration records in a small town yielded the following table of the number of males and females ed as Democrat, Republican, or some other affiliation. Democrat Republican Other
Male Female 300 600 500 300 200 100
2. The proportion of males that are ed as Democrats is (a) 300. (b) 0.33. (c) 0.30.
(d) 0.15.
(e) 0.375.
3. The proportion of all voters who are male and ed as Democrats is (a) 300. (b) 0.33. (c) 0.30. (d) 0.15.
(e) 0.375.
4. Recent data show that states that spend an above-average amount of money X per pupil in high school tend to have below-average mean Verbal SAT scores Y of all students taking the SAT in the state. In other words, there is a negative association between X and Y. This is particularly true in states that have a large percent of all high school students taking the exam. Such states also tend to have larger populations. The most plausible explanation for this association is (a) X causes Y. Overspending generally leads to extra, unnecessary programs, diverting attention from basic subjects. Inadequate training in these subjects generally leads to lower SAT scores. (b) Y causes X. Low SAT scores creates concerns about the quality of education. This inevitably leads to additional spending to help solve the problem. (c) changes in X and Y are due to a common response to other variables. If a higher percent of students take the exam, the average score will be lower. Also, states with larger populations have large urban areas where the cost of living is higher and more money is needed for expenses. (d) changes in X and Y are due to confounding with a third variable. As an example, states in which more money is spent on education tend to be those states with more students living in poverty. As a result, it’s the students’ living conditions that lead to lower SAT Verbal scores, and not the amount spent per pupil. (e) the association between X and Y is purely coincidental. 5. The following two-way table categorizes suicides committed in a particular year by the sex of the victim and the method used. Method Firearms Poison Hanging Other
Male 13,959 3,148 3,222 1,457
Female 2,641 2,469 709 690
Which of the following statements is consistent with the table? (a) There is absolutely no evidence of a relation between the sex of the victim and the method of suicide used. (b) More women commit suicide than men. (c) Men display a greater tendency to use firearms to commit suicide than do women. (d) The correlation between method of suicide and sex of the victim is clearly positive. (e) Females prefer poison over any other method of committing suicide.
Chapter 4
2
Test 4D
Part 2: Free Response Answer completely, but be concise. Show your thought process clearly. 6. The table below presents Census Bureau data on the years of school completed by Americans of different ages. Many people under 25 years of age have not completed their education, so they are left out of the table. The entries in the table are the counts of persons in each age-by-education class. Although both age and education in this table are categorical variables, both have a natural order from least to most. The order of the rows and columns in the table reflects the order of the categories. Years of school completed, by age, 2000 (thousands of persons) Age group Education 25 to 34 35 to 54 55+ Did not complete high school 4,474 9,155 14,224 Completed high school 11,546 26,481 20,060 1 to 3 years of college 10,700 22,618 11,127 4 or more years of college 11,066 23,183 10,596 Total 37,786 81,435 56,008
Total 27,853 58,087 44,445 44,845 175,230
(a) Calculate the marginal distribution of education level.
(b) Calculate the conditional distribution of age group, given “did not complete high school.”
(c) Make a bar graph to display the conditional distribution from (b). Be sure to label your graph.
(d) Describe what the graph in (c) tells you.
Chapter 4
3
Test 4D
7. An experiment was conducted to determine the effect of practice time (in seconds) on the percent of unfamiliar words recalled. Here is a Fathom scatterplot of the results with a least-squares regression line superimposed. (a) Sketch a residual plot below.
(b) Does a linear model fit the data well? Justify your answer.
We used Fathom to transform the original data in hopes of achieving linearity. The screen shots below show the results of two different transformations.
(c) Would an exponential model or a power model fit the original data better? Justify your answer.
(d) Use the model you chose in (c) to predict word recall for 25 seconds of practice. Show your method.
Chapter 4
4
Test 4D
8. From tax records, it is relatively easy to determine the amount of liquor consumed per person and the number of cigarettes consumed per person for each of the 10 provinces of Canada. These are plotted on a scatterplot and a high positive correlation is found. Is the association between these two variables most likely due to causation, confounding, or common response? Justify your answer.
9. A company decided to expand, so it opened a new factory with 455 available jobs. The following tables summarize the hiring decisions made by the company. Workers Managers Male Female Male Female Applied 400 100 Applied 200 200 Hired 300 85 Hired 30 40 (a) Calculate the percent of male and female workers that are hired. Then do likewise for male and female managers.
(b) Use the tables above to create a two-way table that shows the relationship between gender and hiring decision.
(c) Calculate the percent of male and female applicants that were hired.
(d) Explain your findings in (a) and (c).
I pledge that I have neither given nor received aid on this test._____________________________ Chapter 4
5
Test 4D
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