# Chapter 12

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question
A jeweler was interested in the relationship between the weight of a diamond, in carats, and the market price of the diamond, in dollars. The jeweler selected a random sample of diamonds with the same cut and quality and recorded the weight and market price of each diamond. Which of the following residual plots provides evidence that the condition that there is a linear relationship between weight and market price has not been met?
ski slope from left to right
question
A linear regression model was fit to a set of data containing 18 observations. The computer output of the regression analysis is shown in the table. TermCoefSE CoefTConstant12.005.432.210x0.6940.2412.880 Assume the conditions for regression are met. Which of the following defines the margin of error when a 95 percent confidence interval for the slope of the least-squares regression line is calculated?
(2.12)(0.241)
question
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. Based on the residual plot, which condition for inference for the slope of the regression line does not appear to be satisfied?
The standard deviation of the distribution of time to be seated is the same for each size of the dining party.
question
A researcher was interested in the relationship between the number of texts sent in a day and the number of e-mails sent in a day by employees at a certain company. Using 15 data values, a 90 percent confidence interval for the slope of a regression model was found to be ( 2.31, 3.47 ). The researcher claims that the interval would have been narrower with a different sample size if all other things remained the same. Which of the following sample sizes would make the researcher's claim NOT true?
14
question
A research study indicated a negative linear relationship between two variables: the number of hours per week spent exercising (exercise time) and the number of seconds it takes to run one lap around a track (running time). Computer output from the study is shown below. Assuming that all conditions for inference are met, which of the following is an appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals 0 ?
t=0.07?2.20?
question
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 ) The confidence interval is based on a random sample of n 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?
We are 95 percent confident that the true slope of the regression line relating grams of carbohydrates and kilocalories per 100-gram sample of various raw foods is between 2.505 and 6.696.
question
Biologists are interested in how temperature changes might affect the frequency of mating calls of frogs. Twenty gray tree frogs are randomly chosen for a study. For each frog, the temperature of its habitat (in degrees Celsius) and the frequency of its mating call (in tones per second) are recorded. The 96 percent confidence interval for estimating the population slope of the linear regression line predicting mating call frequency based on habitat temperature is given by 2.341±0.768.2.341±0.768. Assume that the conditions for inference for the slope of the regression line have been met. Which of the following is the correct interpretation of the calculated confidence interval?
We are 96 percent confident that the average increase in mating call frequency in the population of frogs when habitat temperature increases by 1 degree Celsius is between 1.573 and 3.109 tones per second.
question
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?
The standard deviation of y does not vary as x varies.
question
A high school basketball coach wants to see whether there is a linear relationship between player height, x, and the number of points scored in a game by basketball players in the coach's state, y. The 96 percent confidence interval to estimate the slope of the linear regression line relating player height to points scored in a game is calculated to be ( -.0.432, 1.844 ). Assume all conditions for inference for the slope of a regression line were met. Based on the confidence interval, which of the following claims is supported by the confidence interval?
It cannot be determined whether the linear relationship between player height and number of points scored for basketball players in the coach's state is positive or negative.
question
A seafood festival organizer is interested in whether there is a relationship between the number of ingredients in the clam chowders that are entered in the festival's clam chowder contest and the ratings given to the chowders by the judges. The organizer requires each of the twelve restaurants in the competition to list all of its chowder's ingredients and requires each judge who tastes the clam chowders to rate each chowder from one through ten on a note card. The organizer then randomly selects twenty-five note cards. Assuming that all conditions for inference are met, which of the following significance tests should be used to investigate whether having more ingredients in the chowders is associated with a reduction in the ratings given to the chowders by the judges?
NOT A chi-square test of independence NOT A two-sample z-test for a difference between proportions
question
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. Assuming the conditions for inference have been met, which of the following inference procedures is most appropriate for this investigation?
NOT A one-sample t-test for means NOT A two-sample z-interval for a difference between proportions
question
A student working on a physics project investigated the relationship between 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 21 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. Based on the residual plot, which condition appears to have been violated?
NOT The errors are independent. NOT The sum of the residuals is 0.
question
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. Which of the following represents a 98 percent confidence interval for the slope of the least-squares regression line for brain shrinkage on blood sugar levels? Assume the conditions for inference are met.
0.161 ± 2.528(0.073)
question
A computer engineer is investigating whether the amount of installed RAM (random access memory) can be used to predict the mean cost of a laptop with the operating system. The computer engineer collected a sample of 20 laptops with the same operating system. The engineer wants to estimate the mean change in the cost, in dollars, for each increase of 1 gigabyte of installed RAM. Assuming the conditions for inference have been met, which of the following inference procedures is the most appropriate for such an investigation?
linear regression t-interval for slope
question
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. Ho:?1=0Ho?:?1?=0 Ha:?1?0Ha?:?1??=0 The test yielded a t-value of 2.186 with a corresponding p-value of 0.044. Which of the following is the correct interpretation of the p-value?
If there is not a linear relationship between overall mileage and the suggested retail price of a car, the probability of observing a test statistic at least as extreme as 2.186 is 0.044.
question
musician songs streaming service recording sales 50 songs
If the null hypothesis is true, the probability of observing a test statistic of 1.592 or greater is 0.059.
question
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?
Ho?:?1?=0 Ha:?1<0Ha?:?1?<0
question
A zoologist selected 12 black bears in a Canadian habitat at random to examine the relationship between the age in years, x, and the weight in tens of pounds, y.. 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±0.570.1.272±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?
We are 95 percent confident that the mean increase in the weight of a black bear for each one-year increase in the age of the bear is between 7.0 and 18.4 pounds.
question
The yield of a certain chemical reaction is believed to be related to temperature. A study collected the yield from 15 such reactions selected at random to test the belief and produced the following results. Variable Estimate Intercept115.52.96Temp10.050.017 R-sq = 0.73 Let ?1?1? represent the slope of the population regression line used to predict the yield of the reaction from the temperature. A t-test for a slope of a regression line was conducted for the following hypotheses. Ho:?1=0Ho?:?1?=0 Ha:?1?0Ha?:?1??=0 Which of the following is the appropriate test statistic for the test?
NOT t=0.730.05? NOT t=15.50.05?
question
A doctor recorded the number of miles walked each day by patients over age 60 and the number of doctor visits in a year for 40 patients. The resulting data were used to conduct a hypothesis test to determine whether there is a linear relationship between the number of miles walked and the number of doctor visits. What are the correct hypotheses for the test?
Ho?:?1?=0 Ha:?1?0Ha?:?1??=0
question
eliza confidence intervals slope of regression line residual plot
I and II only
question
The number of shots taken and points scored by 8 players in a basketball game are shown in the table. Number of shots taken147810111114Number of points scored048914121522 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?
A linear regression t-interval for slope
question
To investigate the relationship between the selling price of a house, y , in dollars, and the size of the house x, in square feet, a local builder collected data on a random sample of 120 houses from a certain region. Assume that the conditions for inference for the slope of a regression line are met. The resulting 95 percent confidence interval for the population slope of the regression line relating price and size is given by ( 62, 99 ). The local builder claims that the selling price of houses from the region increases by \$104 for every extra square foot of space in the house. Which of the following best describes the conclusion that can be reached about this claim based on the confidence interval?
NOT The claim is supported by the interval, since all values in the interval are positive. NOT The claim is supported by the interval, since the interval does not contain the value 104. NOT The claim is not supported by the interval, since the interval does not contain the value 0. NOT The claim is supported by the interval, since the interval does not contain the value 0.
question
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 4 feet 6 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 31 felled trees. EstimateStd Errort valuePr(>|t|)Intercept62.0314.38314.150.0000Diameter1.0540.3223.270.0028 Which of the following is a 95 percent confidence interval for the slope of the population regression line?
( 0.396, 1.712 )
question
researcher cholesterol random calculated standard error of the slope
NOT t = 0.38
question
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. TermCoefSE CoefConstant28.340.945Femur length1.730.023 Assume that the conditions for inference for the slope of the regression equation have been met. Which of the following defines the margin of error for a 99.5 percent confidence interval for the slope of the least-squares regression equation?
3.119(0.023)
question
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 inference on the slope of a regression line shows that they are met. A 98 percent confidence interval for the slope of the regression line relating life expectancy for men, x, and women, y, is given by ( 1.01, 1.34 ). Based on the interval, which of the following claims is supported?
Since the values in the interval are positive, it can be concluded that there is an increase, on average, in the life expectancies of women for each 1-year increase in the life expectancy of men in nonindustrialized countries.
question
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. Amber wants to compute a 95 percent confidence interval for the slope of the least squares regression line in the population of all students in her major field of study. Assuming that conditions for inference are satisfied, which of the following gives the margin of error for the confidence interval?
(2.228)(0.745)
question
credit card linear relationship internal rating customer's credit risk
If the null hypothesis is true, the probability of observing a test statistic at least as extreme as 3.34 is 0.001.
question
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. TermCoefSE CoefTConstant39.884.249.41Time to fatigue3.920.715.52 Which of the following is a 90 percent confidence interval for the slope of the regression line relating performance score and time to fatigue? Assume that the conditions for inference are met.
3.92±1.734(0.71)3.92±1.734(0.71)
question
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?
NOT The slope of the sample regression line is 1.348. NOT The sum of the residuals for the data based on the regression line is positive.
question
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. Assume all conditions for inference were met. Based on the results shown in the table, which of the following is a 95 percent confidence interval for the average change in total cost for each increase of 1 item purchased?
NOT 1.882±2.262(6.6854) NOT 2.784±2.262(11?0.2265?) NOT 2.784±12.29(0.2265)
question
A random sample of 15 college soccer players were selected to investigate the relationship between heart rate and maximal oxygen uptake. The heart rate and maximal oxygen uptake were recorded for each player during a training session. A regression analysis of the data was conducted, where heart rate is the explanatory variable and maximal oxygen uptake is the response variable. If a 95 percent confidence interval is constructed for the slope of the population regression line, which of the following is a condition that must be checked?
The true relationship between heart rate and maximal oxygen uptake is linear.
question
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. VariableDFEstimateSEIntercept1162.073Intentional Walks10.500.037 R-sq = 0.63 Let ?1?1? represent the slope of the population regression line used to predict the number of runs scored from the number of intentional walks in the population of baseball players. A t-test for a slope of a regression line was conducted for the following hypotheses. Ho:?1=0Ho?:?1?=0 Ha:?1?0Ha?:?1??=0 What is the appropriate test statistic for the test?
NOT t=0.630.50? NOT t=2.07316?
question
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 agronomist collected data and used the data to test the claim that there is a linear relationship at a significance level of ?=0.05?=0.05. The agronomist tested the following hypotheses. Ho:?1=0Ho?:?1?=0 Ha:?1?0Ha?:?1??=0 This test yielded a p-value of 0.25. Which of the following is a correct conclusion about the claim?
The null hypothesis is not rejected because 0.25 > 0.05. There is not sufficient evidence to suggest that there is a linear relationship between a wheat stalk's height and its yield.
question
A driving instructor is investigating whether the time a driver spends in a driver's education course improves their score on the driver's test. The instructor randomly selected 10 drivers from a driver's education course and recorded the number of hours each driver attended the driver's education course and their corresponding score on the driver's test. Assuming all conditions for inference are met, which of the following significance tests should be used for the investigation?
NOT A two-sample t-test for a difference between means NOT A matched pairs t-test for a mean difference
question
A fitness center offers a one-month program designed to reduce body fat through exercise. The table shows the body fat percentage before and after completing the program for 10 randomly selected participants. The director of the program wants to investigate whether knowing the body fat percentage before beginning the program can help to predict body fat percentage for someone who completes the program. Which of the following procedures is the most appropriate for such an investigation?
A linear regression t-test for slope
question
A scientist selected a random sample of seven varieties of peach ice cream to investigate the relationship between the density, in pounds per cubic inch, of the varieties of ice cream and the percent concentration of peaches in the ice cream. Assuming all conditions for inference are met, which of the following significance tests should be used to investigate whether there is convincing evidence at the 0.05 level of significance that a greater percent of peaches in the ice cream is associated with an increase in the density of the ice cream?
NOT A chi-square test of independence NOT A two-sample t-test for a difference between means NOT A two-sample z-test for a difference between proportions
question
Researchers believed that an increase in lean body mass is associated with an increase in maximal oxygen uptake. A scatterplot of the measurements taken from 18 randomly selected college athletes displayed a strong positive linear relationship between the two variables. A significance test for the null hypothesis that the slope of the regression line is 0 versus the alternative that the slope is greater than 0 yielded a p-value of 0.04. Which statement is an appropriate conclusion for the test?
NOT The strong positive linear relationship displayed in the scatterplot along with a p-value less than 0.05 indicates that an increase in lean body mass causes an increase in maximal oxygen uptake for college athletes. NOT The p-value of 0.04 indicates that 4% of the variation in maximal oxygen uptake for college athletes can be explained by the amount of lean body mass. NOT A p-value less than 0.05 indicates that the relationship displayed in the scatterplot is likely due to chance, and that there is no statistical evidence of a relationship between lean body mass and maximal oxygen uptake for college athletes.
question
lake runoff factor scientist
NOT The null hypothesis is not rejected since 0.02 < 0.05. There is not sufficient evidence to suggest that there is a linear relationship between a lake's flow rate and runoff factor. NOT The null hypothesis is accepted since 0.02 < 0.05. There is sufficient evidence to suggest that there is not a linear relationship between a lake's flow rate and runoff factor. NOT The null hypothesis is accepted since 0.02 < 0.05. There is sufficient evidence to suggest that there is not a linear relationship between a lake's flow rate and runoff factor.
question
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, yielding the output below. Assuming that all conditions for inference are met, which of the following expressions represents a 95 percent confidence interval for the slope of the least squares regression line?
NOT 1.096±2.086(22?103.995?)
question
Meteorologists are interested in the relationship between minimum pressure and maximum wind speed of hurricanes. The minimum pressure, in millibars, and maximum wind speed, in knots, were collected for a random sample of 100 hurricanes from the year 1995 to the year 2012. A regression analysis of maximum wind speed on minimum wind pressure produced a 95 percent confidence interval of (-1.42, -1.20) for the slope of the least-squares regression line. Which statement is a correct interpretation of the interval?
We can be 95% confident that wind speed decreases, on average, between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure.
question
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?
Ho?:?1?=0 Ha:?1>0Ha?:?1?>0
question
Which of the following would be an indication that the normality condition has been met for a t-test for the slope of a regression model? A residual plot with no apparent pattern in the residuals A histogram of the residuals that is centered at 0, unimodal, and symmetric A dotplot of the residuals that is centered at 0 and strongly skewed to the left with outliers
NOT I, II, and III
question
A statistician constructed the 95 percent confidence interval ( 2.3, 3.7 ) to estimate the slope of a regression model for a set of bivariate data with 24 data values. If the sample size n changes but all other things remain the same, which of the following claims about the confidence interval is true?
NOT The interval width remains the same if n = 28.
question
A statistics teacher wants to determine whether there is a linear relationship 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. Provided that the assumptions for regression inference are satisfied, which of the following provides a 95 percent confidence interval estimate of the slope of the population regression line for predicting foot length from height?
0.583±(2.080)(0.138)
question
A scatterplot of student height, in inches, versus corresponding arm span length, in inches, is shown below. One of the points in the graph is labeled A. If the point labeled A is removed, which of the following statements would be true?
The slope of the least squares regression line increases and the correlation coefficient increases.
question
carbon dioxide emissions fuel efficiency certain car model
446
question
A restaurant manager collected data to predict monthly sales for the restaurant from monthly advertising expenses. The model created from the data showed that 36 percent of the variation in monthly sales could be explained by monthly advertising expenses. What was the value of the correlation coefficient?
0.60
question
The height and age of each child in a random sample of children was recorded. The value of the correlation coefficient between height and age for the children in the sample was 0.8. Based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?
The proportion of the variation in height that is explained by a regression on age is 0.64.
question
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?(y?)=7.3?1.5xlog(y?)=7.3?1.5x. Which of the following is closest to the predicted value of the response variable for x=4.8?x=
1.26
question
Which of the following statements about a least-squares regression analysis is true? A point with a large residual is an outlier. A point with high leverage has a y-value that is not consistent with the other y-values in the set. The removal of an influential point from a data set could change the value of the correlation coefficient.
III only
question
An agriculturalist working with Australian pine trees wanted to investigate the relationship between the age and the height of the Australian pine. A random sample of Australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. Based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the Australian pine based on the age, in years, of the tree. predicted height = 0.29 + 0.48(age) Which of the following is the best interpretation of the slope of the regression line?
The height increases, on average, by 0.48 meter each year.
question
A researcher studying a specific type of tree creates a least-squares regression line for relating the height and the diameter, both in meters, of a fully grown tree. The results are shown in the following computer output. VariableDFEstimateSETIntercept154.002.50Diameter1302.5013.20 Which of the following values represents the predicted change in the height of the tree for each one-meter increase in the diameter of the tree?
30
question
The height h and collar size c, both in centimeters, measured from a sample of boys were used to create the regression line c?=?94+0.9hc?=?94+0.9h. The line is used to predict collar size from height, both in centimeters, for boys' shirt collars. Which of the following has no logical interpretation in context?
The c-intercept of the regression line
question
The following scatterplot shows two variables, x and y, along with a least-squares model. Which of the following is a high leverage point with respect to the regression?