AP Statistics Review Chapters 7-8 Practice Problems Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Suppose you were to collect data for the pair of given variables in order to make a scatterplot. Determine for each variable if it is the explanatory variable, the response variable, or whether it could be both. 1) Teacher: weekly salary, teacher: years of experience 1) A) Teacher: weekly salary: both Teacher: years of experience: both B) Teacher: weekly salary: response Teacher: years of experience: explanatory C) Teacher: weekly salary: both Teacher: years of experience: explanatory D) Teacher: weekly salary: explanatory Teacher: years of experience: both E) Teacher: weekly salary: explanatory Teacher: years of experience: response Suppose you are to form a scatterplot by collecting data for the given pair of variables. Determine the likely direction, form, and strength. 2) Depth, water pressure 2) A) Positive, straight, strong B) Negative, straight, moderate C) Positive, nonlinear, moderate D) Negative, nonlinear, moderate E) Positive, no form, strong Determine whether the scatterplot shows little or no association, a negative association, a positive association, a linear association, a moderately strong association, or a very strong association (multiple associations are possible). 3) 3) A) Linear association B) Linear association, moderately strong association C) Positive association, moderately strong association D) Positive association E) Positive association, moderately strong association, linear association 1
Several scatterplots are given with calculated correlations. Which is which? 4) 1) 2) 4) 3) 4) a) -0.928, b) -0.411, c) 0.002, d) 0.711 A) 1d, 2a, 3b, 4c B) 1a, 2b, 3c, 4d C)1b, 2c, 3d, 4a D) 1c, 2a, 3d, 4c E) 1c, 2d, 3a, 4b Find the correlation. 5) A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below. 5) Number of hours spent in lab Grade (percent) 10 96 11 51 16 62 9 58 7 89 15 81 16 46 10 51 A) 0.371 B) 0.462 C) 0.017 D) -0.335 E) -0.284 2
Solve the problem. 6) A science instructor assigns a group of students to investigate the linear relationship between the ph of the water of a river and its water's hardness (measured in grains). Some students wrote these conclusions: "My correlation of -0.94 shows that there is almost no association between ph of the water and water's hardness." Is the interpretation of the correlation appropriate? A) Yes: a correlation of -0.94 shows a weak relation in a negative direction. B) Yes: ph and hardness of water do not have the same units. C)No: a correlation of -0.94 shows a strong relation in a negative direction. D) No: correlation is always positive. E) No: the ph and the hardness of the water are data collected from the same river. 6) 7) A survey was conducted in 20 counties to determine the percentage of teenagers who had used marijuana and other drugs. Data shown on the following scatterplot indicate a correlation of 0.945 between the percent of teens who have used marijuana and the percent who have used other drugs. Describe the association. 7) A) I am not familiar with any of these drugs. Therefore, I cannot understand B) Strong linear relation in a positive direction C) Strong curved relation in a positive direction D) No evidence of relation E) Weak linear relation in a positive direction 3
8) Data collected from students in Statistics classes included their heights (in inches) and weights (in pounds). For the students' heights and weights, the correlation is 0.636. Suppose the variable weight is recorded in kilograms rather than in pounds. What will be the correlation? 8) A) 0.636 B) 0.636 in./kg C) 0.636 kg/in. D) -0.636 E) 1.401 in./kg Find the lurking variable. 9) A study shows that the amount of chocolate consumed in Canada and the number of automobile accidents is positively related. Find the lurking variable, if there is one. A) Children B) Vacation C) Population growth D) Speed E) No lurking variable 9) Provide an appropriate response. 10) All but one of the statements below contain a mistake. Which one could be true? A) The correlation between age and weight of a newborn baby is r = 0.83 ounces per day. B) The correlation between blood alcohol level and reaction time is r = 0.73. C)The correlation between a person's age and vision (20/20?) is r = -1.04. D) The correlation between the species of tree and its height is r = 0.56. E) There is a high correlation between cigarette smoking and gender. 10) Fill in the missing information. 11) _ x sx _ y sy r y = b0 + b1x 11)?? 20 3-0.6 y = 30-4x A) x = 10; sx = 1.80 B) x = -50; sx = 12.50 C)x = 50; sx = -15.00 D) x = 2.5; sx = 0.45 E) x = 12.5; sx = 0.90 4
Tell what the residual plot indicates about the appropriateness of the linear model that was fit to the data. 12) 12) A) Model is not appropriate. The relationship is nonlinear. B) Model is appropriate. C) Model may not be appropriate. The spread is changing. Answer the question appropriately. 13) A random sample of records of electricity usage of homes gives the amount of electricity used in July and size (in square feet) of 135 homes. A regression to predict the amount of electricity used (in kilowatt-hours) from size was completed. The residuals plot indicated that a linear model is appropriate. What are the variables and units in this regression? A) Amount of electricity used (in kilowatt-hours) is y and number of homes is x. B) Size (in square feet) is y and amount of electricity used (in kilowatt-hours) is x. C)Number of homes is y and amount of electricity used (in kilowatt-hours) is x. D) Amount of electricity used (in kilowatt-hours) is y and size (in square feet) is x. E) Size (in square feet) is y and number of homes is x. 13) 14) If you create a regression model for estimating the price of a salad based upon its weight (oz), is the slope most likely to be 0.2, 2, 20, 200, or 2000? A) 2,000 B) 0.2 C) 200,000 D) 2,000,000 E) 200 14) 15) A random sample of records of electricity usage of homes gives the amount of electricity used in July and size (in square feet) of 135 homes. A regression was done to predict the amount of electricity used (in kilowatt-hours) from size. The residuals plot indicated that a linear model is appropriate. Do you think the slope is positive or negative? Why? A) Negative. Larger homes should use less electricity. B) Positive. More square feet indicates more houses. C) Positive. The larger the number of houses the more electricity used. D) Negative. Smaller homes should use less electricity. E) Positive. Larger homes should use more electricity. 15) 5
16) A random sample of 150 yachts sold in the United States last year was taken. A regression to predict the price (in thousands of dollars) from length (in feet) has an R2 = 15.30%. What would you predict about the price of the yacht whose length was one standard deviation above the mean? A) The price should be 1 SD below the mean in price. B) The price should be 0.391 SDs above the mean in price. C)The price should be 0.782 SDs above the mean in price. D) The price should be 1 SD above the mean in price. E) The price should be 0.920 SDs above the mean in price. 17) The relationship between the number of games won by a minor league baseball team and the average attendance at their home games is analyzed. A regression to predict the average attendance from the number of games won has an R2 = 32.0%. The residuals plot indicated that a linear model is appropriate. Write a sentence summarizing what R2 says about this regression. A) Differences in average attendance explain 32.0% of the variation in the number of games won. B) The number of games won explains 68% of the variation in average attendance. C) The number of games won explains 32.0% of the variation in average attendance. D) Differences in average attendance explain 68% of the variation in the number of games won. E) In 32.0% of games won the attendance was at least as large as the average attendance. 16) 17) Use the model to make the appropriate prediction. 18) A golf ball is dropped from 15 different heights (in inches) and the height of the bounce is recorded (in inches.) The regression analysis gives the model bounce = -0.2 + 0.72 drop. Predict the height of the bounce if dropped from 81 inches. A) 58.32 inches B) 58.12 inches C) 58.52 inches D) 112.78 inches E) 81.52 inches 18) Answer the question appropriately. 19) A random sample of records of electricity usage of homes in the month of July gives the amount of electricity used and size (in square feet) of 135 homes. A regression was done to predict the amount of electricity used (in kilowatt-hours) from size. The residuals plot indicated that a linear model is appropriate. The model is usage= 1254 + 0.7 size. What would a negative residual mean for people living in a house that is 2284 square feet? A) Their house is bigger than expected. B) They are using less electricity than expected. C)They are using the least amount of electricity of all of the houses sampled. D) They are using more electricity than expected. E) Their house is smaller than expected. 20) A golf ball is dropped from 15 different heights (in inches) and the height of the bounce is recorded (in inches.) The regression analysis gives the model bounce = -0.5 + 0.72 drop. A golf ball dropped from 82 inches bounced 60.54 inches. What is the residual for this bounce height.? A) 2 inches B) -2 inches C) 61.04 inches D) 1.44 inches E) 3 inches 19) 20) 6
Explain what is wrong with each interpretation. Assume calculations are done correctly. 21) A biology student does a study to investigate the association between the amount of sunlight and the number of roses on a rosebush in one summer. (The R2 value is 58%) He claims that the amount of sunlight determines 58% of the number of roses on a rosebush in one summer. A) The amount of variation in sunlight changes 58% of the time. This tells us nothing about the number of roses. B) The amount of sunlight will increase the number of roses 58% of the time. C)The amount of sunlight accounts for 58% of the variation in the number of roses. It does not determine the number of roses. D) There is nothing wrong with the interpretation. E) The R2 has to be greater than 90% to make a statement like this. 21) Use the given data to find the equation of the regression line. Round to 3 significant digits, if necessary. 22) Ten Ford Escort classified ads were selected. The age and prices of several used Ford Escorts are given in the table. 22) A) price B) price C) price D) price E) price Age (years) Price 1 $10,000 2 $8500 2 $8000 3 $6000 3 $5900 4 $5800 4 $5000 5 $3000 6 $2000 6 $1900 = -1580 + 11300 age = 10000-1600 age = 7.05-0.000616 age = 11300-1580 age = 7200-692 age Answer the question appropriately. 23) A regression analysis of students' college grade point averages (GPAs) and their high school GPAs found R2 = 0.311. Which of these is true? I. High school GPA accounts for 31.1% of college GPA. II. 31.1% of college GPAs can be correctly predicted with this model. III. 31.1% of the variance in college GPA can be accounted for by the model A) None B) III only C)II only D) I only E) I and II 23) 7
24) When using midterm exam scores to predict a student's final grade in a class, the student would prefer to have a A) residual equal to zero, because that means the student's final grade is exactly what we would predict with the model. B) positive residual, because that means the student's final grade is lower than we would predict with the model. C) negative residual, because that means the student's final grade is lower than we would predict with the model. D) negative residual, because that means the student's final grade is higher than we would predict with the model. E) positive residual, because that means the student's final grade is higher than we would predict with the model. 24) 8
Answer Key Testname: CHAPTERS 7-8 REVIEW 1) B 2) A 3) E 4) E 5) D 6) C 7) B 8) A 9) C 10) B 11) D 12) C 13) D 14) B 15) E 16) B 17) C 18) B 19) B 20) A 21) C 22) D 23) B 24) E 9