Question: The following table shows the average SAT
The following table shows the average SAT Math and Critical Reading scores for students in a sample of states. A scatterplot for these two variables suggests a linear trend. (Source: qsleap.com)
a. Find and report the value for the correlation coefficient and the regression equation for predicting the math score from the critical reading score, rounding off to two decimal places. Then find the predicted math score for a state with a critical reading score of 600.
b. Find and report the value of the correlation coefficient and the regression equation for predicting the critical reading score from the math score. Then find the predicted reading score for a state with a math score of 600.
c. Discuss the effect of changing the choice of dependent and independent variable on the value of r and on the regression equation.
> Use the data in exercise 5.21 to answer the following: a. If a person is chosen randomly from this group, what is the probability that the person is an Independent and said “Yes”? b. If a person is chosen randomly from this group, what is the probability
> A Gallup poll asked a sample of voters if marijuana should be legalized. Voters’ responses and political party affiliation are in the table. (Source: Gallup.com) a. If a person is randomly selected from this group, find the probability
> The Pew Research Center asked a sample of adults if they had read a book in any format in the previous 12 months. The results are shown in the table. (Source: Pewinternet.org) a. If a person is randomly selected from this group, find the probability of
> The Gallup poll asked respondents if they had taken a vacation in the last year. The respondents were separated into two groups: those who had graduated from college and those who had not. Numbers in the table are based on sample sizes of 250 in each gro
> If one card is selected from a well-shuffled deck of 52 cards, what is the probability that the card will be a club OR a diamond OR a heart? What is the probability of the complement of this event? (Refer to exercise 5.11 for information about cards.)
> What is the probability that a baby will be born on a Friday OR a Saturday OR a Sunday if all the days of the week are equally likely as birthdays?
> The sample space shows all possible sequences of child gender for a family with 3 children. The table is organized by the number of girls in the family a. How many outcomes are in the sample space? b. If we assume all outcomes in the sample space are eq
> Make a two-way table from Table 1A for gender and living situation. Put the labels Male and Female across the top and Dorm and Commuter on the side and then tally the data. See page 38 for guidance. a. Report how many are in each cell. b. Find the sums
> The sample space given here shows all possible sequences for tossing a fair coin 4 times. The sequences have been organized by the number of tails in the sequence. a. How many outcomes are in the sample space? b. Assuming all of the outcomes in the samp
> Consider a multiple-choice test with a total of four possible options for each question. a. What is the probability of guessing correctly on one question? (Assume that there are three incorrect options and one correct option.) b. What is the probability
> a. On a true/false quiz in which you are guessing, what is the probability of guessing correctly on one question? b. What is the probability that a guess on one true/false question will be incorrect?
> Refer to exercise 5.11 for information about cards. If you draw one card randomly from a standard 52-card playing deck, what is the probability that it will be the following: a. A black card b. A diamond c. A face card (jack, queen, or king) d. A nine e.
> There are four suits: clubs ( ), diamonds ( ), hearts ( ), and spades ( ), and the following cards appear in each suit: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king. The jack, queen, and king are called face cards because they have a drawing of a f
> For each of the values, state whether the number could be the probability of an event. Give a reason for your answers. a. 99% b. 0.9 c. 9.9 d. 0.0099 e. -0.90
> For each of the values, state whether the number could be the probability of an event. Give a reason for your answers. a. 0.26 b. -0.26 c. 2.6 d. 2.6% e. 26
> A recent Pew Research poll asked respondents to fill in the blank to this question: “The country ____ when it comes to giving equal rights to women” with one of three choices. The results are shown in the following t
> A person is selected randomly from the entire group whose responses are summarized in the table for exercise 5.41. We want to find the probability that the person selected is a male who said “hasn’t gone far enough.” a. Which of the following statements
> The scatterplot shows the median weekly earning (by quarter) for men and women in the United States for the years from 2005 through 2017. The correlation is 0.974. (Source: Bureau of Labor Statistics) a. Use the scatterplot to estimate the median weekly
> Find the frequency, proportion, and percentage of brown-haired people in Table 1A on page 31.
> The graph shows the heights of mothers and daughters. (Source: StatCrunch: Mother and Daughter Heights.xls. Owner: craig_slinkman) a. As the data are graphed, which is the independent variable and which the dependent variable? b. From the graph, approxi
> The scatterplot shows the median starting salaries and the median mid-career salaries for graduates at a selection of colleges. (Source: The Wall Street Journal, Salary increase by salary type, http://online.wsj.com/public/resources/documents/info-Salari
> The following table shows the number of text messages sent and received by some people in one day. (Source: StatCrunch: Responses to survey how often do you text? Owner: Webster West. A subset was used.) a. Make a scatterplot of the data, and state the s
> The table shows the Earned Run Average (ERA) and WHIP rating (walks plus hits per inning) for the top 40 Major League Baseball pitchers in the 2017 season. Top pitchers will tend to have low ERA and WHIP ratings. (Source: ESPN.com) a. Make a scatterplot
> The following table give the Rotten Tomatoes and Metacritic scores for the several movies produced in 2017. Both of these ratings systems give movies a score using a scale from 0 to 100. (Source: vox.com) a. Use technology to make a scatterplot using Rot
> The following table gives the number of millionaires (in thousands) and the population (in hundreds of thousands) for the states in the northeastern region of the United States in 2008. The numbers of millionaires come from Forbes Magazine in March 2007.
> The following table gives the distance from Boston to each city and the cost of a train ticket from Boston to that city for a certain date. a. Use technology to produce a scatterplot. Based on your scatterplot do you think there is a strong linear relat
> The following table gives the distance from Boston to each city (in thousands of miles) and gives the time for one randomly chosen, commercial airplane to make that flight. Do a complete regression analysis that includes a scatterplot with the line, inte
> The graph shows the monthly premiums for a 10-year $250,000 male life insurance policy by age of purchase. For example, a 20-year-old male could purchase such a policy for about $10 per month, while a 50-year-old male would pay about $24 per month for th
> The following graph shows the average car insurance premium for a sample of ages. (Source: valuepenguin.com) a. Explain what the graph tells us about insurance rates for drivers at different ages. Explain why insurance rates might follow this trend. b. W
> Find the frequency, proportion, and percentage of women in Table 1A on page 31.
> The following figure shows a scatterplot with a regression line. The data are for the 50 states. The predictor is the percentage of adults who smoke. The response is the percentage of high school students who smoke. (The point in the lower left is Utah.)
> The following figure shows a scatterplot with the regression line. The data are for the 50 states. The predictor is the percentage of smoke free homes. The response is the percentage of high school students who smoke. The data came from the Centers for D
> Indicate which variable you think should be the predictor (x) and which variable should be the response (y). Explain your choices. a. A researcher measures subjects’ stress levels and blood pressures. b. Workers who commute by car record the length of th
> Indicate which variable you think should be the predictor (x) and which variable should be the response (y). Explain your choices. a. You have collected data on used cars for sale. The variables are price and odometer readings of the cars. b. Research is
> The figure shows a scatterplot of the height of the left seat of a seesaw and the height of the right seat of the same seesaw. Estimate the numerical value of the correlation, and explain the reason for your estimate.
> The following graph shows the winning percentages in singles matches and doubles matches for a sample of male professional tennis players. (Source: tennis.com) a. Based on this scatterplot, would you say there is a strong linear association between these
> The scatterplot shows a solid blue line for predicting weight from age of men; the dotted red line is for predicting weight from age of women. The data were collected from a large statistics class. a. Which line is higher and what does that mean? b. Whic
> The correlation between height and armspan in a sample of adult women was found to be r = 0.948. The correlation between arm span and height in a sample of adult men was found to be r = 0.868. Assuming both associations are linear, which association—the
> Measurements were made for a sample of adult men. Assume that the association between their hand length and foot length is linear. Output for predicting foot length from hand length is provided from several different statistical technologies. a. Report t
> Measurements were made for a sample of adult men. A regression line was fit to predict the men’s arm span from their height. The output from several different statistical technologies is provided. The scatterplot confirms that the assoc
> a. A hospital employs 346 nurses, and 35% of them are male. How many male nurses are there? b. An engineering firm employs 178 engineers, and 112 of them are male. What percentage of these engineers are female? c. A large law firm is made up of 65% male
> The computer output shown below is for predicting foot length from hand length (in centimeters) for a group of women. Assume the trend is linear. Summary statistics for the data are shown in the table below. a. Report the regression equation, using the
> TI-84 output from a linear model for predicting arm span (in centimeters) from height (in inches) is given in the figure. Summary statistics are also provided. To do parts a through c, assume that the association between arm span and height is linear.
> The scatterplot shows the size (in square feet) and selling prices for homes in a certain zip code in California. (Source: realtor.com) a. Use the graph to estimate the selling price of a home with 2000 square feet. b. Use the equation to predict the sel
> If there is a positive correlation between number of years studying math and shoe size (for children), does that prove that larger shoes cause more studying of math or vice versa? Can you think of a confounding variable that might be influencing both of
> Answer the questions using complete sentences. a. An economist noted the correlation between consumer confidence and monthly personal savings was negative. As consumer confidence increases, would we expect monthly personal savings to increase, decrease,
> What is an influential point? How should influential points be treated when doing a regression analysis? b. What is the coefficient of determination and what does it measure? c. What is extrapolation? Should extrapolation ever be used? Answer the questio
> Assume that in a sociology class, the teacher gives a midterm exam and a final exam. Assume that the association between midterm and final scores is linear. Here are the summary statistics: a. Find and report the equation of the regression line to predi
> Assume that in a political science class, the teacher gives a midterm exam and a final exam. Assume that the association between midterm and final scores is linear. The summary statistics have been simplified for clarity see Guidance on page 209. Accord
> Data from the National Data shown in the table are the 4th-grade reading and math scores for a sample of states from the National Assessment of Educational Progress. The scores represent the percentage of 4thgraders in each state who scored at or above b
> Suppose you wanted to know whether living situation was associated with number of units the student had acquired. Could you do that with this data table? If so, which variables would you use?
> Data on the 3-point percentage, field-goal percentage, and free-throw percentage for a sample of 50 professional basketball players were obtained. Regression analyses were conducted on the relationships between 3-point percentage and field-goal percentag
> Data on the number of home runs, strikeouts, and batting averages for a sample of 50 Major League Baseball players were obtained. Regression analyses were conducted on the relationships between home runs and strikeouts and between home runs and batting a
> Data were collected that included information on the weight of the trash (in pounds) on the street for one week and the number of people who live in the house. The following figure shows a scatterplot with the regression line. a. Is the trend positive or
> Grades on a political science test and the number of hours of paid work in the week before the test were recorded. The instructor was trying to predict the grade on a test from the hours of work. The following figure shows a scatterplot and the regressio
> The scatterplot shows the average teacher pay and high school graduation percentage rate for each of the 50 states and the District of Columbia. The regression equation is also shown. (Source: 2017 World Almanac Book of Facts and higheredinfo.org) a. Ba
> The scatterplot shows the average teacher pay and the per pupil expenditure for each of the 50 states and the District of Columbia. The regression equation is also shown. (Source: The 2017 World Almanac and Book of Facts). a. From the scatterplot is the
> The table shows the calories in a five-ounce serving and the % alcohol content for a sample of wines. (Source: healthalicious.com) a. Make a scatterplot using % alcohol as the independent variable and calories as the dependent variable. Include the regr
> The following table shows the weights and prices of some turkeys at different supermarkets. a. Make a scatterplot with weight on the x-axis and cost on the y-axis. Include the regression line on your scatterplot. b. Find the numerical value for the corre
> The following figure shows the relationship between the number of miles per gallon on the highway and that in the city for some cars. a. Report the slope and explain what it means. b. Either interpret the intercept (7.792) or explain why it is not approp
> The equation for the regression line relating the salary and the year first employed is given above the figure. a. Report the slope and explain what it means. b. Either interpret the intercept (4,255,000) or explain why it is not appropriate to interpret
> Suppose a surfer wanted to learn if surfing during a certain time of day made one less likely to be attacked by a shark. Using the Shark Attacks Worldwide data set, which variables could the surfer use in order to answer this question?
> Suppose a doctor telephones those patients who are in the highest 10% with regard to their recently recorded blood pressure and asks them to return for a clinical review. When she retakes their blood pressures, will those new blood pressures, as a group
> Some investors use a technique called the “Dogs of the Dow” to invest. They pick several stocks that are performing poorly from the Dow Jones group (which is a composite of 30 well known stocks) and invest in these. Explain why these stocks will probably
> Does a correlation of -0.70 or +0.50 give a larger coefficient of determination? We say that the linear relationship that has the larger coefficient of determination is more strongly correlated. Which of the values shows a stronger correlation?
> If the correlation between height and weight of a large group of people is 0.67, find the coefficient of determination (as a percentage) and explain what it means. Assume that height is the predictor and weight is the response, and assume that the associ
> Suppose that the growth rate of children looks like a straight line if the height of a child is observed at the ages of 24 months, 28 months, 32 months, and 36 months. If you use the regression obtained from these ages and predict the height of the child
> The scatterplot shows the LSAT (Law School Aptitude Test) scores for a sample of law schools and the percent of students who were employed immediately after law school graduation. Do you think the correlation coefficient among these variables is positive
> The figure shows a scatterplot of birthrate (live births per 1000 women) and the age of the mother in the United States. Would it make sense to find the correlation for this data set? Explain. According to this graph, at approximately what age does the h
> The first scatterplot shows the college tuition and percentage acceptance at some colleges in Massachusetts. Would it make sense to find the correlation using this data set? Why or why not? b. The second scatterplot shows the composite grade on the ACT
> United Press International published an article with the headline “Study Finds Correlation between Educations, Life Expectancy.” Would you expect this correlation to be negative or positive? Explain your reasoning in the context of this headline.
> USA Today College published an article with the headline “Positive Correlation Found between Gym Usage and GPA.” Explain what a positive correlation means in the context of this headline.
> A data set on Shark Attacks Worldwide posted on Stat Crunch records data on all shark attacks in recorded history including attacks before 1800. Variables contained in the data include time of attack, date, location, activity the victim was engaged in wh
> College students who were drivers were asked if they had ever received a speeding ticket (yes or no). The results are shown in the table, along with gender. a. There are two variables in the table, state what they are and whether each is categorical or n
> Five people were asked how many female first cousins they had and how many male first cousins. The data are shown in the table. Assume the trend is linear, find the correlation, and comment on what it means.
> Seth Wagerman, a former professor at California Lutheran University, went to the website RateMyProfessors.com and looked up the quality rating and also the “easiness” of the six full-time professors in one department.
> The correlation between house price (in dollars) and area of the house (in square feet) for some houses is 0.91. If you found the correlation between house price in thousands of dollars and area in square feet for the same houses, what would the correlat
> In Exercise 4.1 there is a graph of the relationship between SAT score and college GPA. SAT score was the predictor and college GPA was the response variable. If you reverse the variables so that college GPA was the predictor and SAT score was the respon
> The table for part (a) shows distances between selected cities and the cost of a business class train ticket for travel between these cities. a. Calculate the correlation coefficient for the data shown in the table by using a computer or statistical calc
> The distance (in kilometers) and price (in dollars) for one-way airline tickets from San Francisco to several cities are shown in the table. a. Find the correlation coefficient for this data using a computer or statistical calculator. Use distance as th
> Match each of the following correlations with the corresponding graph. -0.51 _________ 0.98 _________ 0.18 _________
> Match each of the following correlations with the corresponding graph. 0.87 _________ -0.47 _________ 0.67 _________ (Source: StatCrunch: 2011 MLB Pitching Stats according to owner: IrishBlazeFighter) (Source: StatCrunch: 2011 MLB Pitching Stats accor
> Pick the letter of the graph that goes with each numerical value listed below for the correlation. Correlations: -0.903 _________ 0.374 _________ 0.777 _________
> Pick the letter of the graph that goes with each numerical value listed below for the correlation. Correlations: 0.767 _________ 0.299 _________ -0.980 ________
> Suppose you wanted to know whether ring size and height were associated. Could you do that with this data table? If so, which variables would you use?
> The scatterplot shows the acceptance rate and selectivity index for a sample of medical schools. The acceptance rate is the percentage of applicants who were accepted into the medical school. The selectivity index is a measure based on GPA, test scores,
> The first graph shows the years a person was employed before working at the company and the salary at the company. The second graph shows the years employed at the company and the salary. Which graph shows a stronger relationship and could do a better jo
> The scatterplots show SAT scores and GPA in college for a sample of students. The top graph uses the critical reading SAT score to predict GPA in college and the bottom graph shows math SAT to predict GPA. Which is the better predictor of GPA for these s
> The figure shows a scatterplot of the heights and weights of some women taking statistics. Describe what you see. Is the trend positive, negative, or near zero? Explain.
> The scatterplot shows the age and number of hours of sleep “last night” for some students. Do you think the trend is slightly positive or slightly negative? What does that mean?
> The scatterplot shows the number of hours of work per week and the number of hours of sleep per night for some college students. Does the graph show a strong increasing trend, a strong decreasing trend, or very little trend? Explain.
> The scatterplot shows the number of work hours and the number of TV hours per week for some college students who work. There is a very slight trend. Is the trend positive or negative? What does the direction of the trend mean in this context? Identify an
> Describe the trend in the scatterplot of house price and area for some houses. State which point appears to be an outlier that does not fit the rest of the data.
> The scatterplot shows the numbers of brothers and sisters for a large number of students. Do you think the trend is somewhat positive or somewhat negative? What does the direction (positive or negative) of the trend mean? Does the direction make sense in
> The scatterplot shows data on salary and years of education for a sample of workers. Comment on the trend of the scatterplot. Is the trend positive, negative, or near zero?
> Suppose you wanted to know whether living situation was associated with number of hours of study per week. Could you do that with this data table? If so, which variables would you use?
> The scatterplot shows data on credits attained and GPA for a sample of college students. Comment on the trend of the scatterplot. Is the trend positive, negative, or near zero?
> The scatterplot shows data on age and GPA for a sample of college students. Comment on the trend of the scatterplot. Is the trend positive, negative, or near zero?
> The scatterplot below shows data on age of a sample students and the number of college credits attained. Comment on the strength, direction, and shape of the trend.
> The data shows the number of calories, carbohydrates (in grams) and sugar (in grams) found in a selection of menu items at McDonald’s. Scatterplots suggest the relationship between calories and both carbs and sugars is linear. The data
