Based on data obtained from the CIA World Factbook, the linear correlation coefficient between the number of television stations in a country and the life expectancy of residents of the country is 0.599. What does this correlation imply? Do you believe that the more television stations a country has, the longer its population can expect to live? Why or why not? What is a likely lurking variable between number of televisions and life expectancy?
> Explain why it does not make sense to find a least-squares regression line for the Bear Market data from Problem 34 in Section 4.1.
> Given a choice, would you conduct a study using an observational study or a designed experiment? Why?
> Explain why it does not make sense to find a least-squares regression line for the CEO Performance data from Problem 33 in Section 4.1.
> An engineer wants to determine how the weight of a car, x, affects gas mileage, y. The following data represent the weights of various domestic cars and their miles per gallon in the city for the 2015 model year. (a) Find the least-squares regression lin
> Example 5 in Section 4.1 on page 178 discussed the effect of cola consumption on bone mineral density in the femoral neck of women. (a) Find the least-squares regression line treating cola consumption per week as the explanatory variable. (b) Interpret t
> The following data represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean. (a) Find the least-squares regression line treating atmospheric pressure as t
> The following data represent the speed at which a ball was hit (in miles per hour) and the distance it traveled (in feet) for a random sample of home runs in a Major League baseball game. (a) Find the least-squares regression line treating speed at which
> The American black bear (Ursus americanus) is one of eight bear species in the world. It is the smallest North American bear and the most common bear species on the planet. In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-te
> A pediatrician wants to determine the relation that exists between a child’s height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the following data. (a) Fin
> An economist wants to determine the relation between one’s FICO score, x, and the interest rate of a 36-month auto loan, y. The given data represent the interest rate (in percent) a bank would offer on a 36-month auto loan for various FICO scores. (a) Fi
> The following data represent commute times (in minutes) and score on a well-being survey. (a) Find the least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable. (b) Interpret
> The least- squares regression equation / relates the carbon dioxide emissions (in millions of tonnes), y, and electricity produced (terrawatt-hours), x, for all countries in the world. Source: www.bp.com (a) Interpret the slope. (b) The lowest electric e
> Which type of study allows the researcher to claim causation between an explanatory variable and a response variable?
> Is there a relation between the age difference between husband/wives and the percent of a country that is literate. Researchers found the least-squares regression between age difference (husband age minus wife age), y, and literacy rate (percent of the p
> After the first exam in a statistics course, Professor Katula surveyed 14 randomly selected students to determine the relation between the amount of time they spent studying for the exam and exam score. She found that a linear relation exists between the
> In Problem 15 from Section 4.1, a scatter diagram and correlation coefficient suggested there is a linear relation between the percentage of individuals who have at least a bachelor’s degree and median income in the states. In fact, the least-squares reg
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> For the data set (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that / and r = 0.957241, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter
> Match each type of study to its definition.
> For the data set (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that / and r = -0.9477, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter
> If the linear correlation coefficient is 0, what is the equation of the least-squares regression line?
> Which of the following is true of the least-squares regression line / (a) The predicted value of / is an estimate of the mean value of the response variable for a particular value of the explanatory variable. (b) The predicted value of /is an estimate
> State the properties of the linear correlation coefficient.
> What does it mean to say two variables are positively associated? Negatively associated?
> A____ is a graph that shows the relation between two quantitative variables.
> The ____variable is the variable whose value can be explained by the value of the explanatory variable
> What is the difference between univariate data and bivariate data?
> Suppose that two variables, X and Y, are negatively associated. Does this mean that above-average values of X will always be associated with below-average values of Y? Explain.
> Suppose you work a part-time job and earn $15 per hour. Draw a scatter diagram that might represent the relation between your gross pay and hours worked. Is this a deterministic relation or a probabilistic relation?
> Match each word or phrase with its definition.
> Draw a scatter diagram that might represent the relation between the number of minutes spent exercising on an elliptical and calories burned. Draw a scatter diagram that might represent the relation between number of hours each week spent on Facebook and
> Explain the difference between correlation and causation. When is it appropriate to state that the correlation implies causation?
> Write a paragraph that explains the concept of correlation. Include a discussion of the role that/play in the computation.
> Explain what is wrong with the following statement: “We have concluded that a high correlation exists between the gender of drivers and rates of automobile accidents.” Suggest a better way to write the sentence.
> What does it mean if r = 0?
> What does it mean to say that the linear correlation coefficient between two variables equals 1? What would the scatter diagram look like?
> Professors Theodore Coladarci and Irv Kornfield from the University of Maine found a correlation of 0.68 between responses to questions on the RateMyProfessors.com website and typical in-class evaluations. Use this correlation to make an argument in fa
> Go to www.pearsonhighered.com/ sullivanstats to obtain the data file 4_1_49 using the file format of your choice for the version of the text you are using. The data represent the cost, return on investment, and graduation rate for a random sample of 50 c
> Consider the following data set: (a) Draw a scatter diagram with the x-axis starting at 0 and ending at 30 and with the y-axis starting at 0 and ending at 20. (b) Compute the linear correlation coefficient. (c) Now multiply both x and y by 2. (d) Draw a
> Consider the following set of data: (a) Draw a scatter diagram of the data and compute the linear correlation coefficient. (b) Draw a scatter diagram of the data and compute the linear correlation coefficient with the additional data point (10.4, 9.3). C
> The age of a person is commonly considered to be a continuous random variable. Could it be considered a discrete random variable instead? Explain.
> On the basis of the scatter diagram below, explain what is wrong with the following statement: “Because the linear correlation coefficient between age and median income is 0.012, there is no relation between age and median income.”
> The linear correlation between violent crime rate and percentage of the population that has a cell phone is -0.918 for years since 1995. Do you believe that increasing the percentage of the population that has a cell phone will decrease the violent crime
> In a study published in the Journal of the American Medical Association, researchers found that the length of time a mother breast-feeds is negatively associated with the likelihood a child is obese. In an interview, the head investigator stated, “It’s n
> Lyme disease is an inflammatory disease that results in a skin rash and flulike symptoms. It is transmitted through the bite of an infected deer tick. The following data represent the number of reported cases of Lyme disease and the number of drowning de
> One basic theory of investing is diversification. The idea is that you want to have a basket of stocks that do not all “move in the same direction.” In other words, if one investment goes down, you don’t want a second investment in your portfolio that is
> The ultimate goal in any sport (besides having fun) is to win. One measure of how well a team does is winning percentage. In baseball, a lot of effort goes into figuring out the variables that help to predict a team’s winning percentage. Go to www.pearso
> Consider the four data sets shown below. (a) Compute the linear correlation coefficient for each data set. (b) Draw a scatter diagram for each data set. Conclude that linear correlation coefficients and scatter diagrams must be used together in any stati
> The website that contained the American black bear data listed in Problem 30 actually had a bear whose length is 141.0 cm and weight is 100 kg, but incorrectly listed its length as 41.0 cm. (a) Redraw the scatter diagram with the incorrect entry. (b) Rec
> An engineer wants to determine how the weight of a car affects gas mileage. The following data represent the weights of various domestic cars and their gas mileages in the city for the 2015 model year. (a) Determine which variable is the likely explanato
> Explain the process of statistics.
> The following data represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. (a) On the same graph, draw a scatter diagram for both males and females. Be sure to use a different plott
> Researchers wondered whether the size of a person’s brain was related to the individual’s mental capacity. They selected a sample of right-handed introductory psychology students who had SAT scores higher than 1350. The subjects took the Wechsler Adult I
> The following data represent the total compensation for 12 randomly selected chief executive officers (CEO) and the company’s stock performance in 2017. (a) One would think that a higher stock return would lead to a higher compensation. Based on this, wh
> The data in the next column represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean. (a) Draw a scatter diagram treating atmospheric pressure as the expla
> The following data represent the speed at which a ball was hit (in miles per hour) and the distance it traveled (in feet) for a random sample of home runs in a Major League baseball game. (a) A researcher wants to determine if the speed with which the ba
> The American black bear (Ursus americanus) is one of eight bear species in the world. It is the smallest North American bear and the most common bear species on the planet. In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-te
> A pediatrician wants to determine the relation that may exist between a child’s height and head circumference. She randomly selects eleven 3-year-old children from her practice, measures their heights and head circumference, and obtains the data shown in
> Your Fair Isaacs Corporation (FICO) credit score is used to determine your creditworthiness. It is used to help determine whether you qualify for a mortgage or credit and is even used to determine insurance rates. FICO scores have a range of 300 to 850,
> The Gallup Organization regularly surveys adult Americans regarding their commute time to work. In addition, they administer a Well-Being Survey. According to the Gallup Organization, “The Gallup-Healthways Well-Being Index Composite Score is comprised o
> For the 41 nations that participated in TIMMS, the correlation between the percentage of students who skipped class at least once in the past month and the mean score on the exam was -0.52. Does this suggest there is a linear relation between attendance
> Explain what is meant when we say “data vary.” How does this variability affect the results of statistical analysis?
> The Trends in International Mathematics and Science (TIMMS) is a mathematics and science achievement exam given internationally. On each exam, students are asked to respond to a variety of background questions. For the 41 nations that participated in T
> Put the following correlation coefficients in order from weakest to strongest in terms of strength of linear association. -1, 0.377, 0.084, -0.436, 0.444, -0.733
> Put the following correlation coefficients in order from weakest to strongest in terms of strength of linear association. -0.903, 0.339, -0.431, 0.137, 0.869
> For each of the following statements, explain whether you think the variables will have positive correlation, negative correlation, or no correlation. Support your opinion. (a) Number of cigarettes smoked by a pregnant woman each week and birth weight of
> For each of the following statements, explain whether you think the variables will have positive correlation, negative correlation, or no correlation. Support your opinion. (a) Number of children in the household under the age of 3 and expenditures on di
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> The scatter diagram in the next column drawn in StatCrunch shows the relation between percent of the population with at least a bachelor’s degree in a state and birthrate (births per 1000 women 15 to 44 years old). (a) Describe any relation that exists b
> In your own words, define the four levels of measurement of a variable. Give an example of each.
> The scatter diagram drawn in Minitab shows the relation between the percentage of the population of a state plus Washington, DC, that has at least a bachelor’s degree and the median income (in dollars) of the state for 2017. Source: U.S. Census Bureau. (
> Match the linear correlation coefficient to the scatter diagram. The scales on the x- and y-axes are the same for each diagram. (a) r = -0.969 (b) r = -0.049 (c) r = -1 (d) r = -0.992
> Match the linear correlation coefficient to the scatter diagram. The scales on the x- and y-axes are the same for each diagram. (a) r = 0.787 (b) r = -0.787 (c) r = -0.053 (d) r = 0.946
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> True or False: Correlation implies causation.
> A _____ variable is a variable that is related to both the explanatory and response variable.
> True or False: If the linear correlation coefficient is close to 0, then the two variables have no relation.
> Contrast the differences between qualitative and quantitative variables. Discuss the differences between discrete and continuous variables.
> In a boxplot, if the median is to the left of the center of the box and the right whisker is substantially longer than the left whisker, the distribution is skewed________ .
> What does the five-number summary consist of?
> Explain how to determine the shape of a distribution using the boxplot and quartiles.
> Which boxplot shown to the right likely has the data with a larger standard deviation? Why?
> Does hunger improve strategic decision making? That is, if you are hungry are you more likely to make a favorable decision when the outcome of your decision is uncertain (as in business decisions)? To test this theory, researchers randomly divided 30 nor
> The data set “Tornadoes_2017” located at www.pearsonhighered.com/sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017. (a) Draw side-by-side boxplots of length of the tornado by month. Which mont
> Open the data 3_5_19 at www.pearsonhighered.com/sullivanstats. This data represents the amount of time of a cab ride (in seconds), the fare collected, and the payment method for a random sample of 100 rides in the City of Chicago. Source: Chicago Data Po
> It is well- documented that active maternal smoking during pregnancy is associated with lower-birth-weight babies. Researchers wanted to determine if there is a relationship between paternal smoking habits and birth weight. The researchers administered
> In April, 2014, the city of Flint, Michigan stopped buying water that came from Lake Huron and started using water from the Flint River to save money. After the move, residents of Flint started experiencing symptoms that could be attributed to the consum
> Do store-brand chocolate chip cookies have fewer chips per cookie than Keebler’s Chips Deluxe Chocolate Chip Cookies? To find out, a student randomly selected 21 cookies of each brand and counted the number of chips in the cookies. The results are shown
> Explain the difference between a population and a sample.
