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Chapter 12 AP stats Questions with Solutions
1. An agronomist is an expert in soil management and crop production. A certain state
hires an agronomist to investigate whether there is a linear relationship between a wheat stalk's height and the yield of wheat. The agron- omist collected data and used the data to test the claim that there is a linear relationship at a significance level of ±=0.0 5 ±=0.05. The agronomist tested the following hypotheses.: D
2. A scientist is investigating whether percent concentration can be used to predict
density in apple juice. A scientist selected a random sample of 12 apple juice varieties and recorded the density, in pounds per cubic inch, and the percent concentration of each apple juice variety. The scientist wants to estimate the mean change in the density, in pounds per cubic inch, for each increase of 1 percent concentration of apple juice.: A. A linear regression t-interval for slope
3. A baseball enthusiast carried out a simple linear regression to investigate whether
there is a linear relationship between the number of runs scored by a player and the number of times the player was intentionally walked. Computer output from the regression analysis is shown.: E. t=0.50/0.
4. The number of shots taken and points scored by 8 players in a basketball game are
shown in the table. A basketball coach is investigating whether the number of shots
taken can be used to predict the mean number of points scored. Assuming the conditions for inference have been met, which of the following inference procedures is the most appropriate to estimate the mean change in the number of points scored for each increase of 1 shot taken?: B
5. A zoologist selected 12 black bears in a Canadian habitat at random to examine the
relationship between the age in years, xx, and the weight in tens of pounds, yy. The 95 percent confidence interval for estimating the population slope of the linear regression line predicting weight in tens of pounds based on the age in years is given by 1.272±0.5701.272±0.570. Assume that the conditions for inference for the slope of the regression equation are met. Which of the following is the correct interpretation of the interval?: A
6. A car retailer wanted to see if there is a linear relationship between overall mileage
and the suggested retail price of a car. The retailer collected data on 18 cars of a similar type selected at random and used the data to test the claim that there is a linear relationship. The following hypotheses were used to test the claim.: B
7. The yield of a certain chemical reaction is believed to be related to temper- ature. A
study collected the yield from 15 such reactions selected at random to test the belief and produced the following results.: E. t=0.05/0.
8. A researcher collected data on the cholesterol level, CC, and the age, AA, of 24
people selected at random. Using the data, the researcher calculated the least-squares
11. A student working on a physics project investigated the relationship be- tween the
speed and the height of roller coasters. The student collected data on the maximum speed, in miles per hour, and the maximum height, in feet, for a random sample of 2121 roller coasters, with the intent of testing the slope of the linear relationship between maximum speed and maximum height. However, based on the residual plot shown, the conditions for such a test might not be met.: E. The variance of the response variable is constant for all values of the explanatory variable.
12. As part of a class project at a large university, Amber selected a random sample of
12 students in her major field of study. All students in the sample were asked to report their number of hours spent studying for the final exam and their score on the final exam. A regression analysis on the data produced the following partial computer output.: A
13. Raoul performed an experiment using 16 windup rubber band single-pro- peller
airplanes. He wound up the propeller a different number of times and recorded the amount of time (in seconds) that the airplane flew for each number of rotations that the propeller was wound. A regression analysis was performed and the partial computer output is given below.: A
14. Scientists have long believed that linear regression could be used to predict the
brain weight of nonhuman mammals from the body weight. In one study, body weight, in kilograms, and brain weight, in grams, of 22 nonhuman mammals were measured. A
linear regression analysis was performed, yield- ing the output below.: A
15. A statistics teacher wants to determine whether there is a linear relation- ship
between high school students' heights, in inches (in), and the lengths of their feet, in centimeters (cm). The teacher obtains height and foot-length measurements for a random sample of 23 students at the high school and generates the following graph and computer output.: B
16. A major credit card company is interested in whether there is a linear relationship
between its internal rating of a customer's credit risk and that of an independent rating agency. The company collected a random sample of 200 customers and used the data to test the claim that there is a linear relationship. The following hypotheses were used to test the claim.: E
17. A reporter was interested in the relationship between the size of a dining party and
the amount of time it takes for the dining party to be seated at a restaurant. The reporter selected a random sample of dining parties from a certain region. The resulting data were used to complete a linear regression analysis of the time, in minutes, it takes for a dining party to be seated versus the number of people in the dining party. The linear regression analysis produced the residual plot shown.: B. The standard deviation of the distribution of time to be seated is the same for each size of the dining party.
18. A doctor recorded the number of miles walked each day by patients over age 60
course and their corresponding score on the driver's test. Assuming all con- ditions for inference are met, which of the following significance tests should be used for the investigation?: D
20. A teacher conducted a regression analysis to investigate the relationship between
student height and femur length. Computer output from the linear regression analysis is shown in the table. The analysis was performed on a sample of 24 students.: C
21. A 90 percent confidence interval for the slope of a regression line is determined
to be (-0.181, 1.529). Which of the following statements must be true?: A. The correlation coefficient of the data is positive.
22. Data were collected from a longitudinal study designed to investigate the
relationship between blood sugar levels and brain shrinkage. The results of an analysis of the data for 22 observations are shown in the table below.: C
23. A consumer group wanted to investigate the relationship between the number of
items purchased at a single visit to the local grocery store and the total cost of the items purchased. The group obtained a random sample of 11 receipts from the store and recorded the total number of items and the total cost from each receipt. The computer output of an analysis of total cost versus number of items purchased is shown in the table.: B
24. Measuring the height of a tree is usually more difficult than measuring the diameter
of the tree. Therefore, many researchers use regression models to predict the height of a tree from its diameter measured at 44 feet 66 inches from the ground. The following computer output shows the results of a linear regression based on the heights, in feet, and the diameters, in inches, recorded from 3131 felled trees.: B
25. Twenty members of an athletic club are studying the relationship between the time
it takes an individual athlete to reach a given level of fatigue during exercise (time to fatigue, measured in minutes) and athletic performance. For each member, time to fatigue and a performance score were recorded. The computer output of the regression analysis is shown in the table.: C
26. Which of the following statements about a least-squares regression analy- sis is
true?: C III only
27. The following scatterplot shows two variables, xx and yy, along with a least-
squares model. Which of the following is a high leverage point with respect to the regression?- : E. (80,70)
28. An international organization is investigating the relationship between the life
expectancies of men and women in nonindustrialized countries. A random sample of such countries was selected, and life expectancies, in years, were determined for both men and women. A check of the conditions necessary for
claims that the width of the confidence interval will increase if a sample size of 30 is used, all other things remaining the same. Quincy claims that the width of the confidence interval will decrease if a sample size of 30 is used. Which statement is true about the claims made by Peggy and Quincy?: B. Quincy's claim is correct.
34. An exponential relationship exists between the explanatory variable and the
response variable in a set of data. The common logarithm of each value of the response variable is taken, and the least-squares regression line has an equation of log(yˆ)=7.31.5xlog(ay^)=7. 3 1.5x. Which of the following is closest to the predicted value of the response variable for x=4.8x=4.8 ?: D. 1.
35. A 95 percent confidence interval for the slope of the regression line relating the
number of grams of carbohydrates and the number of kilocalories per 100-gram sample of various raw foods is given by (2.505,6.696)(2.505,6.696). The confidence interval is based on a random sample of nn raw foods. A check of the conditions for inference on the slope shows they are reasonably met. Which of the following is a correct interpretation of the interval?: E
36. When computing a confidence interval for the slope of a regression line, a plot of
the residuals versus the fitted values can be used to check which of the following conditions?: B. The standard deviation of yy does not vary as xx varies.
37. Eliza plans on constructing a confidence interval for the slope of a re- gression
line. She creates the residual plot shown to check the conditions for creating the interval. Which of the following conditions appear to be met based on the residual plot?: D. I and II only
38. A researcher recorded the total number of minutes that 25 people spent looking at
either a computer, phone, or television screen during a day and the number of minutes of sleep that they slept that night. The resulting data were used to conduct a hypothesis test to investigate whether there is a negative linear relationship between the total number of minutes spent looking at a screen and the number of minutes of sleep. What are the correct hypotheses for the test?: C
39. The residual plots from five different least squares regression lines are shown
below. Which of the plots provides the strongest evidence that its regression line is an appropriate model for the data and is consistent with the assumptions required for inference for regression?: Graph C
40. A statistician constructed the 95 percent confidence interval (2.3,3.7)(2.3,b- 3.7) to
estimate the slope of a regression model for a set of bivariate data with 24 data values.: D
41. A popular musician believes an increase in the number of times songs are listened
to via a streaming service leads to an increase in recording sales. The musician's recording company selected 50 songs at random and used the data to test the claim
45. Data were collected on two variables, xx and yy, to create a model to predict yy from
xx. A scatterplot of the collected data revealed a curved pattern with a possible cubic relationship (y=ax3y=ax3, where aa is a constant) between the variables. Which of the following transformations would be most appropriate for creating linearity between the variables?: E
46. The relationship between carbon dioxide emissions and fuel efficiency of a
certain car can be modeled by the least-squares regression equation ln(yˆ)=70.045xln(ay^)= 7 0.045x, where xx represents the fuel efficiency, in miles per gallon, and yˆy^ represents the predicted carbon dioxide emissions, in grams per mile. Which of the following is closest to the predicted carbon dioxide emissions, in grams per mile, for a car of this type with a fuel efficiency of 20 miles per gallon?: C. 446
47. An education researcher recorded the number of books students read over the last
year and the number of vocabulary words that students defined correctly on a test of 100 vocabulary words. The resulting data were used to conduct a hypothesis test to investigate whether there is a positive linear relationship between the number of books read and the number of vocabulary words defined correctly. What are the correct hypotheses for the test?: B
48. A car magazine claims that there is a linear relationship between a car's weight, in
pounds, and the car's fuel efficiency, in miles per gallon. The maga- zine collected data and used the data to test the claim at a significance level of ±=0.0 5 ±=0.05. The
magazine tested the following hypotheses.: D
