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Elementary Statistics 11th Edition Robert R. Johnson, Patricia J. Kuby - Solutions
The American Community Survey gathers data for population, demographic, and housing unit estimates. The Census Bureau then uses the data to produce and disseminate official estimates of housing units for states and counties. The 2005€“2007 housing unit estimates for the town of Webster in
Buick and Jaguar tied for first place in the 2009 Vehicle Dependability Study for J.D. Power & Associates. It is an annual survey of three-year-old cars where consumers check off all the problems they have had with their 2006 model-year vehicles. A random sample of the J.D. Power data produced the
The Rochester Raging Rhinos Professional Soccer Team is hoping for a good 2010 season. The blend of experienced and young, energetic players should make for a solid team. The current ages for the team are:a. Construct a grouped frequency histogram using classes 19€“21, 21€“23,
The “average” is a commonly reported statistic. This single bit of information can be very informative or very misleading, with the mean and median being the two most commonly reported. a. The mean is a useful measure, but it can be misleading. Describe a circumstance when the mean is very
All the third graders at Roth Elementary School were given a physical-fitness strength test. These data resulted:a. Construct a dotplot. b. Find the mode. c. Prepare a grouped frequency distribution using classes 1€“4, 4€“7, and so on, and draw a histogram of the distribution.
Consumers are frequently cautioned against eating too much food that is high in calories, fat, and sodium for numerous health and fitness reasons. Nutrition in Action published a list of popular low-fat brands of hot dogs commonly labeled €œfat-free,€€œreduced
The number of runs scored by Major League Baseball teams is likely influenced by whether the game is played at home or at the opponent€™s ballpark. In an attempt to measure differences between playing at home or away, the average number of runs scored per game by each MLB team while
Does everything increase, every year? Sometimes it seems like it! The 2007 annual percentage rate of increase in all motor-fuel consumption by U.S. states was reported in the Highway Statistics, November 2008, and is listed in the table. Notice that the consumption did not increase in every
Students like to engage in the €œBattle of the Sexes€ when it comes to who€™s the better driver. But which gender outnumbers the other on the road? The numbers may surprise you. Listed below is the number of licensed male and female drivers in each of 18 randomly
You are responsible for planning the parking needed for a new 256-unit apartment complex and you’re told to base the needs on the statistic “average number of vehicles per household is 1.9.” a. Which average (mean, median, mode, midrange) will be helpful to you? Explain. b. Explain why
In what states do the residents pay the most taxes? Pay the least? Perhaps it depends on the variable used to measure the amount of taxes paid. In 2008 the Tax Policy Center reported the following statistics about the average annual 2006 taxes and percent of personal income paid per person by
Cleaning behind furniture and washing windows top the list of spring-cleaning chores, according to the Soap and Detergent Association’s (SDA) latest National Spring Cleaning Survey. International Communications Research (ICR) completed the independent consumer research study in January/February
Your instructor and your class have made a deal on the exam just taken and currently being graded. If the class attains a mean score of 74 or better, there will be no homework on the coming weekend. If the class mean is 72 or below, then not only will there be homework as usual but all of the class
Starting with the data values 70 and 100, add three data values to the sample so that the sample has the following: a. Mean of 100 b. Median of 70 c. Mode of 87 d. Midrange of 70 e. Mean of 100 and a median of 70 f. Mean of 100 and a mode of 87 g. Mean of 100 and a midrange of 70 h. Mean of 100, a
In 2008 the Tax Policy Center reported the following statistics about the average annual 2006 taxes and percent of personal income paid per person by state.a. Find the range for the amount of taxes paid per person.b. Find the range for the percentage of personal income paid in taxes per person.
a. The data value 45 has a deviation value of 12. Explain the meaning of this. b. The data value 84 has a deviation value of _20. Explain the meaning of this.
The summation∑(x ) is always zero. Why? Think back to the definition of the mean (p. 63) and see if you can justify this statement.
All measures of variation are nonnegative in value for all sets of data. a. What does it mean for a value to be “nonnegative”? b. Describe the conditions necessary for a measure of variation to have the value zero. c. Describe the conditions necessary for a measure of variation to have a
A sample contains the data {1, 3, 5, 6, 10}. a. Use formula (2.5) to find the variance. b. Use formula (2.9) to find the variance. c. Compare the results from parts a and b.
Consider the sample 2, 4, 7, 8, 9. Find the following: a. Range b. Variance s2, using formula (2.5) c. Standard deviation, s
Consider the sample 6, 8, 7, 5, 3, 7. Find the following: a. Range b. Variance s2, using formula (2.5) c. Standard deviation, s
What effect does the minimum amount have on the interest rate being offered on 3-month certificates of deposit (CDs)? The following are advertised rates of return, y, for a minimum deposit of $500, $1000, $2500, $5000, or $10,000, x. (Note that x is in $100 and y is annual percentage rate of
Sugar cane growers are interested in the relationship between the total acres of sugar cane harvested and the total sugar cane production (tons) of those acres. The data listed here are for the 2007 crop from 14 randomly selected sugar cane€“producing counties in Louisiana.a. These data
Relatively few business travelers use mass transit systems when visiting large cities. The payoff could be substantial€”in both time and money€”if they learned how to use the systems, as noted in the December 28, 2004, USA Today article €œMass transit could save
Cicadas are flying, plant-eating insects. One particular species, 13-year cicadas (Magicicada), spends five juvenile stages in underground burrows. During the 13 years underground, the cicadas grow from approximately the size of a small ant to nearly the size of an adult cicada. Every 13 years, the
Yellowstone National Park€™s Old Faithful has been a major tourist attraction for a long time. Understanding the duration of eruptions and the time between eruptions is necessary to predict the timing of the next eruption. The Old Faithful dataset variables are as follows: date: an index
a. Verify, algebraically, that formula (3.2) for calculating r is equivalent to the definition formula (3.1). b. Verify, algebraically, that formula (3.6) is equivalent to formula (3.5).
a. Verify the equation for these data:
Can a woman€™s height be predicted from her mother€™s height? The heights of some mother€“daughter pairs are listed; x is the mother€™s height and y is the daughter€™s height.a. Draw two dotplots using the same scale and showing the two sets of data
The following tables list the ages, heights (in inches), and weights (in pounds) of the players on the 2009 roster for the National Hockey League teams Boston Bruins and Edmonton Oilers.a. Compare each of the three variables€”height, weight, and age€”using either a dotplot or a
Draw a coordinate axis and plot the points (0, 6), (3, 5), (3, 2), and (5, 0) to form a scatter diagram. Describe the pattern that the data show in this display.
Does studying for an exam pay off?a. Draw a scatter diagram of the number of hours studied, x, compared with the exam grade received, y.b. Explain what you can conclude based on the pattern of data shown on the scatter diagram drawn in part a.
Refer to Figure 3.8 In “Americans Love Their Automobiles” (Applied Example 3.4 On p. 128) to answer the following questions: a. Name the two variables used. b. Does the scatter diagram suggest a relationship between the two variables? Explain. c. What conclusion, if any, can you draw from the
Growth charts are commonly used by a child€™s pediatrician to monitor a child€™s growth. Consider the growth chart that follows.a. What are the two variables shown in the graph? b. What information does the ordered pair (3, 87) represent? c. Describe how the pediatrician might
a. Draw a scatter diagram showing height, x, and weight, y, for the Boston Bruins hockey team, using the data in Exercise 3.12. b. Draw a scatter diagram showing height, x, and weight, y, for the Edmonton Oilers hockey team using the data in Exercise 3.12. c. Explain why the data, as used in parts
The accompanying data show the number of hours, x, studied for an exam and the grade received, y (y is measured in tens; that is, means that the grade, rounded to the nearest 10 points, is 80). Draw the scatter diagram.
a. Is there a relationship between a person’s height and shoe size as he or she grows from an infant to age 16? As one variable gets larger, does the other also get larger? Explain your answers. b. Is there a relationship between height and shoe size for people who are older than 16 years of age?
An experimental psychologist asserts that the older a child is, the fewer irrelevant answers he or she will give during a controlled experiment.To investigate this claim, the following data were collected. Draw a scatter diagram.
A sample of 15 upper-class students who commute to classes was selected at registration. They were asked to estimate the distance (x) and the time (y) required to commute each day to class (see the following table).a. Do you expect to find a linear relationship between the two variables commute
Refer to the 2009 4-wheel-drive, 6-cylinder SUVs chart in Applied Example 3.4 on page 128 and the two variables gas tank capacity, x, and the cost to fill it, y. a. If you were to draw scatter diagrams of these two variables, on the same graph but separate, for the SUVs that use regular and premium
Baseball stadiums vary in age, style and size, and many other ways. Fans might think of the size of a stadium in terms of the number of seats, while players might measure the size of a stadium in terms of the distance from home plate to the centerfield fence.Is there a relationship between these
Most adult Americans drive. But do you have any idea how many licensed drivers there are in each U.S. state? The table here lists the number of male and female drivers licensed in each of 15 randomly selected U.S. states during 2007.a. Do you expect to find a linear (straight-line) relationship
Ronald Fisher, an English statistician (1890€“1962), collected measurements for a sample of 150 irises. Of concern were five variables: species, petal width (PW), petal length (PL), sepal width (SW), and sepal length (SL) (all in mm). Sepals are the outermost leaves that encase the flower
Total solar eclipses actually take place nearly as often as total lunar eclipses, but the former are visible over a much narrower path. Both the path width and the duration vary substantially from one eclipse to the next. The table below shows the duration (in seconds) and path width (in miles) of
In a national survey of 500 business and 500 leisure travelers, each was asked where he or she would most like €œmore space.€a. Express the table as percentages of the total. b. Express the table as percentages of the row totals. Why might one prefer the table to be expressed
Does studying for an exam pay off? The number of hours studied, x, is compared with the exam grade received, y:a. Complete the preliminary calculations: extensions, five sums, SS(x), SS(y), and SS(xy). b. Find r.
Cell phones and iPods are necessities for the current generation. Does the use of one indicate the use of the other? Seven junior high students who own both a cell phone and an iPod were randomly selected, resulting in the following data:a. Complete the preliminary calculations: extensions, five
Many organizations offer €œspecial€ magazine rates to their members. The American Federation of Teachers is no different, and here are a few of the rates they offer their members.a. Construct a scatter diagram with €œyour price€ as the dependent variable,
A random sample of 10 seventh-grade students gave the following data on of minutes watching television on an average weeknight versus of minutes spent on homework on an average weeknight.a. Construct a scatter diagram with €œhomework minutes€ as the dependent variable, y, and
Manatees swim near the surface of the water. They often run into trouble with the many powerboats in Florida. Consider the graph that follows.a. What two groups of subjects are being compared? b. What two variables are being used to make the comparison? c. What conclusion can one make based on this
Estimate the correlation coefficient for each of the following:
a. Use the scatter diagram you drew in Exercise 3.19 (p. 133) to estimate r for the sample data on the number of hours studied and the exam grade. b. Calculate r.
a. Use the scatter diagram you drew in Exercise 3.20 to estimate r for the sample data on the number of irrelevant answers and the child’s age. b. Calculate r.
A marketing firm wished to determine whether the number of television commercials broadcast was linearly correlated with the sales of its product. The data, obtained from each of several cities, are shown in the following table.a. Draw a scatter diagram. b. Estimate r. c. Calculate r.
The “In the eye of the beholder” graphic shows two circle graphs, each with four sections. This same information could be represented in the form of a 2 × 4contingency table of two qualitative variables. a. Identify the population and name the two variables. b. Construct the contingency table
Movie production companies spend millions of dollars to produce movies, with the great hope of attracting millions of people to the theater.The success of a movie can be measured in many ways, two of which are box office receipts and the number of Oscar nominations received. Below is a list of ten
Consider the following 2009 4WD, 6-Cyl SUV data.a. What value do you anticipate for a correlation coefficient of the two variables annual petroleum consumption in barrels, x, and annual tons of CO2 emitted, y? Explain. b. Calculate the linear correlation coefficient for the two variables annual
The Children€™s Bureau of the U.S. Department of Health and Human Services has a monumental job. In 2006, 510,000 children were in foster care. Of those, approximately 51,000 were adopted. Are more males or more females typically adopted? Is there a difference? The table lists the number
Sports drinks are very popular in today€™s culture around the world.The following table lists 10 different products you can buy in England and the values for three variables: cost per serving (in pence), energy per serving (in kilocalories), and carbohydrates per serving (in grams)a. Draw
During the 2008 MLB All Star Game Home Run Contest, Josh Hamilton put on an amazing show with his 35 home runs. The recorded Apex and Distance of each home run he hit is listed here: Apex€”The highest point reached by the ball in flight above field level, in feet. StdDist, Standard
NBA players, teams, and fans are interested in seeing their leading scorers score lots of points, yet at the same time the number of personal fouls they commit tends to limit their playing time. For the leading scorer on each team, the table lists the number of minutes per game, MPG, and the number
Ever wanted to know the weight of your catch, but didn€™t have a scale? Measure a Muskellunge from the snout to the tip of the tail.The following weights are averages taken from fish collected by DEC fish management crews from across New York State.a. Examine the data and find an
In many communities there is a strong positive correlation between the amount of ice cream sold in a given month and the number of drownings that occur in that month. Does this mean that ice cream causes drowning? If not, can you think of an alternative explanation for the strong association? Write
€œThe perfect age€ graphic shows the results from a 9 × 2 contingency table for one qualitative and one quantitative variable.a. Identify the population and name the qualitative and quantitative variables. b. Construct a bar graph showing the two distributions side
Explain why one would expect to find a positive correlation between the number of fire engines that respond to a fire and the amount of damage done in the fire. Does this mean that the damage would be less extensive if fewer fire engines were dispatched? Explain.
Draw a scatter diagram for these data:Would you be justified in using the techniques of linear regression on these data to find the line of best fit? Explain.
Draw a scatter diagram for these data:Would you be justified in using the techniques of linear regression on these data to find the line of best fit? Explain.
The Children€™s Bureau of the U.S. Department of Health and Human Services has a monu monumental job. In 2006, 510,000 children were in foster care. Of those, approximately 303,000 entered during the 2006 year (10/1/05€“9/20/06). The following table lists the ages of children
The formulas for finding the slope and the y-intercept of the line of best fit use both summations ’s, and sums of squares, SS( )’s. It is important to know the difference. In reference to Example 3.5 (p. 138): a. Find three pairs of values: _x2, SS(x); _y2, SS(y); and _xy, SS(xy). b. Explain
Does it pay to study for an exam? The number of hours studied, x, is compared to the exam grade received, y:a. Find the equation for the line of best fit. b. Draw the line of best fit on the scatter diagram of the data drawn in Exercise 3.15 (p. 133). c. Based on what you see in your answers to
How old is my bass? Ever wondered about the age of the bass you just caught? Measure your bass from the snout to the tip of the tail. The following ages are average ages by length of largemouth and smallmouth bass in New York State.a. Examine the data and find an approximate pattern for age
The values of x used to find points for graphing the line yˆ = 14.9 + 0.66x in Figure 3.24 (p. 149) are arbitrary. Suppose you choose to use x = 20 and x = 50 a. What are the corresponding values? b. Locate these two points on Figure 3.24.Are these points on the line of best fit? Explain why or
If all students from Mr. Chamberlain’s physical fitness course on page 127 who can do 40 push-ups are asked to do as many sit-ups as possible: a. How many sit-ups do you expect that each can do? b Will they all be able to do the same number? c. Explain the meaning of the answer to part a.
What is the relationship between carbohydrates consumed and energy released in a sports drink? Let’s use the sports drink data listed in Exercise 3.45 on page 144 to investigate the relationship. a. In Exercise 3.45 a scatter diagram was drawn using x = carbs/ serving and y = energy / serving.
The National Highway System Designation Act of 1995 allows states to set their own highway speed limits. Most of the states have raised the limits. The November 2008 maximum speed limits on interstate highways (rural) for cars and trucks by each state are given in the following table (in miles per
Referring to Applied Example 3.8 (p. 155): a. Explain (in 25 or more words) what you believe the statement, “The ordered pairs from Table 3.16 and on the scatter diagram, Figure 3.28, are not data values; they are the result of an averaging effect as hundreds of recorded values were summarized”
A.J. used linear regression to help him understand his monthly telephone bill. The line of best fit was yˆ =23.65 + 1.28x where x is the number of long-distance calls made during a month, and y is the total telephone cost for a month. In terms of number of long-distance calls and cost: a. Explain
Geoff is interested in purchasing a moderately priced SUV. He realizes that a car or truck loses its value as soon as it is driven off the dealer’s lot. Geoff uses linear regression to get a better sense of how this decline works.The regression line is yˆ = 34.03 – 3.04x, where x is the age of
For Example 3.7 (p. 150) and the scatter diagram in Figure 3.26 on page 151: a. Explain how the slope of 4.71 can be seen. b. Explain why the y-intercept of-186.5 cannot be seen.
For any basketball player, the number of points scored per game and the number of personal fouls committed are of interest. Data taken for a team last season resulted in the equation yˆ =1.122 +3.394x where x is the number of personal fouls committed per game and y is the number of points scored
A study was conducted to investigate the relationship between the cost, y (in tens of thousands of dollars), per unit of equipment manufactured and the number of units produced per run, x. The resulting equation for the line of best fit was yˆ = 7.31 -0.01x with x being observed for values between
A study was conducted to investigate the relationship between the resale price, y (in hundreds of dollars), and the age, x (in years), of midsize luxury American automobiles. The equation of the line of best fit was determined to be yˆ =185.7 -21.52x a. Find the resale value of such a car when it
The Federal Highway Administration annually reports on state motor-fuel taxes. Based on the latest report, the amount of receipts, in thousands of dollars, can be estimated using the equation: Receipts = - 5359 + 0.9956 Collections. a. If a state collected $500,000, what would you estimate the
A study of the tipping habits of restaurant-goers was completed.The data for two of the variables—x, the amount of the restaurant check, and y, the amount left as a tip for the servers—were used to construct a scatter diagram. a. Do you expect the two variables to show a linear relationship?
Consider Figure 3.27 on page 154. The graph’s yintercept Is – 225 not approximately 80, as might be read from the figure. Explain why.
A statewide survey was conducted to investigate the relationship between viewers€™ preferences for ABC, CBS, NBC, PBS, or FOX for news information and their political party affiliation.The results are shown in tabular form:a. How many viewers were surveyed? b. Why are these bivariate
Consider the College Women’s data presented in Example 3.7 and the line of best fit. When estimating the line of best fit from a scatter diagram, the choice for the two points (x1, y1) and (x2, y2) to be used is somewhat arbitrary. When different points are used, slightly different values for b0
a. If every person€™s arm displayed the exact Golden Ratio, describe the appearance of a scatter diagram where the length of the forearm, y, and the length of the hand, x, have been plotted.b. Since body proportions vary from person to person, describe the appearance of a scatter diagram
€œNow more than ever, a degree matters,€ according to an upstate New York college advertisement in the May 31, 2009, Democrat and Chronicle.The following statistics from the U.S. Bureau of Labor Statistics were presented on median usual weekly earnings.a. Construct a scatter
The U.S. per capita consumption of bottled water has grown continuously since 1997, by more than 1 gallon annually. a. Inspect the data in the chart below and explain how the data show growth of more than 1 gallon annually. b. Construct a scatter diagram using years after 1997, x, and consumption,
Bottled water is big business in the United States, and around the world too. Listed here are annual numbers indicating just how big the U.S. bottled water market is (volume is in gallons and producer revenues are in U.S. dollars).a. Inspect the data in the chart and explain how the numbers show
Baseball teams win and lose games. Many fans believe that a team€™s earned run average (ERA) has a major effect on that team€™s winning.During the 2008 season, the 30 Major League Baseball teams recorded the following numbers of wins while generating these earned run averages:a.
Consider the saying, €œBuild it and they will come.€ This notable saying from a movie may very well apply to shopping malls. Just be sure when you build that there is room for not only the mall but also for those that will come€”and thus include enough space for
Consider the accompanying contingency table, which presents the results of an advertising survey about the use of credit by Martan Oil Company customers.a. How many customers were surveyed? b. Why are these bivariate data? What type of variable is each one? c. How many customers preferred to use an
The given rule of thumb is that pets age seven times faster than people. The most common pets are dogs and cats.a. Consider the data below on cat ages versus human ages. Is there a relationship between cat ages and human ages? Comment on the strength. Calculate the equation for the line of best
The graph on page 162 shows the relationship between three variables: number of licensed drivers, number of registered vehicles, and the size of the resident population in the United States from 1960 to 2007. Study the graph and answer the questions.a. Does it seem reasonable for the population
The correlation coefficient and the slope of the line of best fit are related by definition. a. Verify this statement. b. Describe how the relationship between correlation coefficient and slope can be seen in the statistics that describe a particular set of data. c. Show that b1 = r(sy/sx) Comment
Fear of the dentist (or the dentist€™s chair) is an emotion felt by many people of all ages. A survey of 100 individuals in five age groups was conducted about this fear, and these were the results:a. Find the marginal totals. b. Express the frequencies as percentages of the grand
As summer heats up, Americans turn to ice cream as a way to cool off. One of the questions asked as part of a July 2009 Harris Poll was, €œWhat is your favorite way to eat ice cream?€The study included 2177 U.S. adults.The accompanying €œFavorite Way to Eat Ice
Six breeds of dogs have been rather popular in the United States over the past few years.The table below lists the breeds coupled with the number of registrations of each filed with the American Kennel Club in 2004 and 2005:a. A cross-tabulation of the two variables, year (columns) and dog breed
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