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elementary statistics

Just The Essentials Of Elementary Statistics 10th Edition Robert Johnson, Patricia Kuby - Solutions

[EX03-98] Wildlife populations are monitored with aerial photographs. The number of animals and their locations relative to areas inhabited by the human population are useful information.Sometimes it is possible to monitor the physical characteristics of the animals. The length of an alligator can
[EX03-97] Lakes are bodies of water surrounded by land and may include seas. The accompanying table lists the areas and maximum depths of 32 lakes throughout the world.a. Draw a scatter diagram showing area, x, and maximum depth, y, for the lakes.b. Find the linear correlation coefficient between
[EX03-96] The sound of crickets chirping is a welcome summer night’s sound. In fact, those chirping crickets may be telling you the temperature.In the book The Song of Insects, George W.Pierce, a Harvard physics professor, presented real data relating the number of chirps per second, x, for
[EX03-095] Twenty-four countries were randomly selected from The World Factbook’s 2004 list of world countries. The life expectancies for males and females were recorded for those countries.Country Male Life Expectancy Female Life Expectancy Albania 74.37 80.02 American Samoa 72.05 79.41•••
[EX03-094] A biological study of a minnow called the blacknose dace* was conducted. The length, y (in millimeters), and the age, x (to the nearest year), were recorded.*Visit: http://www.dnr.state.oh.us/dnap/rivfish/bndace.html x 0 3 2 2 1 3 2 4 1 1 y 25 80 45 40 36 75 50 95 30 15a. Draw a scatter
[EX03-093] Major league baseball teams often say they sign players with skills that match the confines of their home stadium, thinking that because half of their games are at home, this will work to their advantage. If this were the case, then it would seem that teams would tend to score more runs
Start with the point (5, 5) and add at least four ordered pairs, (x, y), to make a set of ordered pairs that display the following properties. Show that your sample satisfies the requirements.a. The correlation of x and y is between 0.9 and1.0, and the slope of the line of best fit is 0.5.b. The
A scatter diagram is drawn showing the data for x and y, two normally distributed variables. The data fall within the intervals 20 x40 and 60 y100. Where would you expect to find the data on the scatter diagram, if:a. The correlation coefficient is 0.0b. The correlation coefficient is 0.3c. The
Start with the point (5, 5) and add at least four ordered pairs, (x, y), to make a set of ordered pairs that display the following properties. Show that your sample satisfies the requirements.a. The correlation of x and y is 0.0.b. The correlation of x and y is 1.0.c. The correlation of x and y is
Consider this set of bivariate data:x 1 1 3 3 y 1 3 1 3a. Draw a scatter diagram.b. Calculate the correlation coefficient.c. Calculate the line of best fit.
These data were generated using the equation y 2x 1.x 0 1 2 3 4 y 1 3 5 7 9 A scatter diagram of the data results in five points that fall perfectly on a straight line. Find the correlation coefficient and the equation of the line of best fit.
An automobile owner records the number of gallons of gasoline, x, required to fill the gasoline tank and the number of miles traveled, y, between fill-ups.a. If she does a correlation analysis on the data, what would be her purpose and what would be the nature of her results?b. If she does a
Determine whether each of the following questions requires correlation analysis or regression analysis to obtain an answer.a. Is there a correlation between the grades a student attained in high school and the grades he or she attained in college?b. What is the relationship between the weight of a
[EX03-85] Part of quality control is keeping track of what is occurring. The following contingency table shows the number of rejected castings last month categorized by their cause and the work shift during which they occurred.1st Shift 2nd Shift 3rd Shift Sand 87 110 72 Shift 16 17 4 Drop 12 17 16
[EX03-84] When was the last time you saw your doctor? That question was asked for the survey summarized in the following table.Time Since Last Consultation 6 Months to Less Than Less Than 1 Year 6 Months 1 Year or More Younger than 28 years 413 192 295 Age 28–40 574 208 218 Older than 40 653 288
[EX03-083] Six breeds of dogs have been rather popular in the United States over the past few years. The following table lists the breeds coupled with the number of registrations filed with the American Kennel Club in 2003 and 2004.Breeds 2003 2004 Retrievers (Labrador) 144,896 146,692 Retrievers
[EX03-81] 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:Elementary Jr. High Sr. High College Adult Fear 37 28 25 27 21 Do Not Fear 63 72 75 73
The correlation coefficient and 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 on
Nielsen Ratings are often published in national newspapers. The number of viewers (in millions)for each program is given with the corresponding Nielsen Rating. With the number of viewers as x and the ratings as y, the data published in USA Today (February 7, 2002) for the 7–10 PM time slot
[EX03-077] The Office of Aviation Enforcement& Proceedings, U.S. Department of Transportation, reported the number of mishandled baggage reports filed by airline passengers (in thousands) during October 2004. The industry average was 4.02 reports per 1000 passengers.Airline Reports Passengers
[EX03-076] The success of a professional golfer can be measured along a number of dimensions.The bottom line is probably how much money a golfer earns in a given year, but golfers are also given a world ranking by points for each event that they enter. Following is a combined table extracted from
[TA03-12] By looking at the insurance rates shown in Applied Example 3.6, one can easily see that males pay higher rates for insurance than females of the same age. Is there a consistent pattern to this higher rate? To uncover any such pattern in the male/female $250,000 insurance rates from
[EX03-074] Interstate 90, the longest of the east–west U.S. interstate highways, is 3112 miles long, stretching from Boston, Massachusetts, at I-93 on the eastern end to Seattle, Washington, at the Kingdome on the western end. It travels across 13 northern states; the number of miles and number
[EX03-073] Baseball teams win and lose games. Many fans believe that a team’s earned run average (ERA) has a major effect on winning. During the 2004 season, the 30 major league baseball teams recorded the following number of wins while generating these ERAs.Wins ERA Wins ERA Wins ERA 96 3.74 98
[EX03-072] The following data are a sample of the ages, x (years), and the asking prices, y($1000), for used Honda Accords that were listed on AutoTrader.com on March 10, 2005:x y x y x y 3 24.9 7 11.9 6 16.4 7 9.0 6 15.2 4 21.2 5 17.8 2 25.9 3 24.9 4 29.2 2 26.9 5 20.0 6 15.7 4 23.8 7 13.6 3 24.9
[EX03-071] Professional golfers have a classic golf quandary: “drive for show, putt for dough.”It is often their short game (on the putting green)that determines whether they win a tournament.In the January 7, 2005, USA Today article titled “In short, Durant aims to improve,” a chart was
[EX03-070] Luxury cars are sweet if you can afford them. If not, you may want to consider a more affordable “feel alike” model, according to Mitch McCullough, who evaluates 60 to 70 vehicles annually as editor of New Car Test Drive(http://www.nctd.com).Luxury Models Cost ($1000)Mercedes-Benz
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
[EX03-068] Stride rate (number of steps per second) is important to the serious runner. Stride rate is closely related to speed, and a runner’s goal is to achieve the optimal stride rate. As part of a study, researchers measured the stride rate at seven different speeds for 21 top female
Consider Figure 3.24 on page 182. The graph’s y-intercept is 250, not approximately 80, as might be read from the figure. Explain why?
A study of the tipping habits of restaurantgoers 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. What do you expect the scatter diagram to reveal?a. Do you expect
The Federal Highway Administration annually reports on state motor-fuel taxes. Based on the latest report, in thousands of dollars, the amount of receipts can be estimated using the equation:Receipts5359 0.9956 Collections.a. If a state collected $500,000, what would you estimate the receipts
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 wasˆ y 7.31 0.01x, with x being observed for values
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 ˆ y 185.7 21.52x.a. Find the resale value of such a car when
If all students from Mr. Chamberlain’s physical fitness course on pages 153 and 164 who can do 40 push-ups are asked to do as many sit-ups as possible:a. How many sit-ups do you expect each can do?b Will they all be able to do the same number?c. Explain the meaning of the answer to part a.
For Example 3.7 (p. 177) and the scatter diagram in Figure 3.23 on page 179:a. Explain how the slope of 4.71 can be seen.b. Explain why the y-intercept of 186.5 cannot be seen.
AJ used linear regression to help him understand his monthly telephone bill. The line of best fit was ˆ y 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
[EX03-059] What is the relationship between carbohydrates consumed and energy released in a sports drink? Did you ever wonder if there was a relationship? Let’s use the sports drink data listed in Exercise 3.43 on page 171 to investigate the relationship.a. In Exercise 3.43 a scatter diagram was
Does it pay to study for an exam? The number of hours studied, x, is compared to the exam grade received, y:x 2 5 1 4 2 y 80 80 70 90 60a. 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. 158).c. Based on what you
The values of x used to find points for graphing the line ˆ y 14.9 0.66x in Figure 3.21(p. 177) are arbitrary. Suppose you choose to use x 20 and x 50.a. What are the corresponding ˆ y values?b. Locate these two points on Figure 3.21. Are these points on the line of best fit? Explain why
Show that formula (3.7a) is equivalent to formula (3.7) (p. 175).
The formulas for finding the slope and the yintercept 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. 164):a. Find three pairs of values: x2, SS(x); y2, SS(y); and xy, SS(xy).b. Explain the
[EX03-054] Twenty-four countries were randomly selected from The World Factbook’s 2004 list of world countries. Data on the percentage of each country below the poverty line and the countries’life expectancies were collected.Country Below Poverty Life Expectancy Afghanistan 23.0 42.46 Albania
[EX03-053] Draw a scatter diagram for these data:x 2 12 4 6 9 4 11 3 10 11 3 1 13 12 14 7 2 8 y 4 8 10 9 10 8 8 5 10 9 8 3 9 8 8 11 6 9 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:x 1 2.5 3 4 5 1.5 y 1.5 2.2 3.5 3 4 2.5 Would you be justified in using the techniques of linear regression on these data to find the line of best fit? Explain.
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.
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
[TA03-012] By looking at the insurance rates on the table in Applied Example 3.6, we can see that as a person ages, the insurance rate increases.You probably anticipated that, but let’s take a closer look at one of specific situations listed.a. Calculate the correlation coefficient, r, for the
[EX03-048] NBA players, teams, and fans are interested in seeing their leading scorer score lots of points, yet at the same time, the number of personal fouls they commit tends to limit their playing time. For each team, the following table lists the number of minutes played per game(Min/G) and the
[EX03-047] The national highway system is made up of interstate highways and noninterstate highways. Listed here are 15 randomly selected U.S. states and their corresponding number of miles of interstate and noninterstate highway.National Highway System, Number of Miles—October 2005 State
[EX03-046] 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 the box office receipts and the number of Oscar nominations received.Following
[EX03-045] Interstate 95, the longest of the north–south U.S. interstate highways, is 1907 miles long, stretching from Houlton, Maine, at the Canadian border on the northern end to Miami, Florida, at US 1 on the southern end. It travels across 15 east–coast states; the number of miles and the
[EX03-044] The National Adoption Information Clearinghouse tracks and posts information about adoptions in the United States. The following table lists the number of children adopted in each of 16 randomly identified states for 1991 and 2001.State 1991 2001 State 1991 2001 State 1991 2001 DE 190
[EX03-043] 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
[EX03-040] A marketing firm wished to determine whether the number of television commercials broadcast were linearly correlated with the sales of its product. The data, obtained from each of several cities, are shown in the following table.City A B C D E F G H I J Commercials, x 12 6 9 15 11 15 8
a. Use the scatter diagram you drew in Exercise 3.20 (p. 159) to estimate r for the sample data on the number of irrelevant answers and the child’s age.b. Calculate r.
a. Use the scatter diagram you drew in Exercise 3.19 (p. 159) to estimate r for the sample data on the number of hours studied and the exam grade.b. Calculate r.
[EX03-035] Many organizations offer “special”magazine subscription rates to their members.The American Federation of Teachers is no different, and here are a few of the rates they offer their members.Magazine Usual Rate Your Price Cosmopolitan $29.97 $18.00 Sports Illustrated $78.97 $39.75
Does studying for an exam pay off? The number of hours studied, x, is compared with the exam grade received, y:x 2 5 1 4 2 y 80 80 70 90 60a. Complete the preliminary calculations: extensions, five sums, SS(x), SS(y), and SS(xy).b. Find r.
Explain why it makes sense for a set of data to have a correlation coefficient of zero when the data show a very definite pattern, as in Figure 3.9(p. 163).
How would you interpret the findings of a correlation study that reported a linear correlation coefficient of 0.3?
How would you interpret the findings of a correlation study that reported a linear correlation coefficient of 1.34?
Skillbuilder Applet Exercise provides scatter diagrams for various correlation coefficients.a. Starting at r 0, move the slider to the right until r 1.Explain what is happening to the corresponding scatter diagrams.b. Starting at r 0, move the slider to the left until r1. Explain what is
[EX03-028] Total solar eclipses actually take place nearly as often as total lunar eclipses, but they are visible over a much narrower path. Both the path width and the duration vary substantially from one eclipse to the next. The following table shows the duration (in seconds) and path width(in
[EX03-027] 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
[EX03-026] The following table lists the height (in inches), weight (in pounds), and date of birth of the members of the 2004 Rochester Raging Rhinos professional soccer team.Player Height Weight DOB 1 68 160 12/7/1978 2 71 170 2/2/1970••• Remainder of data on Student’s Suite CD-ROM Source:
[EX03-025] Are people stronger today than they used to be? Can they run faster? Let’s compare the performances of the Olympic gold medal winners for the last century as a way to decide. The distances (in inches) for the gold medal performances in the long jump, high jump, and discus throw are
[EX03-024] Most adult Americans drive.But do you have any idea how many licensed drivers there are in each U.S. state? The following table lists the number of male and female drivers licensed in each of 15 randomly selected U.S. states.Licensed Drivers per State (100,000)Male Female Male Female
[EX03-023] Baseball stadiums vary in age, style, size, and many other ways. Fans might think of the size of the stadium in terms of the number of seats, whereas players might measure the size of the stadium by the distance (in feet) from home plate to the center field fence.Seats CF Seats CF Seats
[EX03-022] A sample of 15 upper-class students who commute to classes was selected at registration.The students were asked to estimate the distance, x (nearest mile), and the time, y (nearest 5 min.), required to commute each day to class(see accompanying table). Construct a scatter diagram
[EX03-021] The following table lists the percents of students who receive free or reduced-price lunches compared with the percents who passed the reading portion of a state exam. The results are for Sandusky County, Ohio, and were reported in The Blade, a Toledo newspaper, on August 5,
[EX03-020] 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. (Retain this solution to use in Exercise 3.39, p 170.)Age,
[EX03-019] 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, y 8 means that the grade, rounded to the nearest 10 points, is 80). Draw the scatter diagram. (Retain this solution to use in Exercise 3.38, p. 170.)x 2 3 3
a. Draw a scatter diagram showing height, x, and weight, y, for the Brazilian World Cup soccer team using the data in Exercise 3.12.b. Draw a scatter diagram showing height, x, and weight, y, for the German World Cup soccer team using the data in Exercise 3.12.c. Explain why the data, as used in
Refer to “Northwest Ohio Schools and How They Rate” (Applied Example 3.4 on p. 154) to answer the following questions:a. What are 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
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.x 2 5 1 4 2 y 80 80 70 90 60b. Explain what you can conclude based on the pattern of data shown on the scatter diagram drawn in parta. (Retain these solutions to
Draw a coordinate axis and plot the points(0, 6), (3, 5), (3, 2), (5, 0) to form a scatter diagram.Describe the pattern that the data show in this display.
Consider the two variables of a person’s height and weight. Which variable, height or weight, would you use as the input variable when studying their relationship? Explain why.
[EX03-012] The following table lists the heights (in meters), weights (in kilograms), and ages of the players on the two teams that played in the 2002 World Cup finals: Brazil and Germany.Brazil Germany Player Height Weight Age Height Weight Age 1 1.93 86 28 1.88 88 33 2 1.95 85 29 1.90 87
[EX03-011] 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.x 63 63 67 65 61 63 61 64 62 63 y 63 65 65 65 64 64 63 62 63 64 x 64 63 64 64 63 67 61 65 64 65 66 y 64 64
[EX03-009] The January 2005 unemployment rate for eastern and western U.S. states was as follows:Eastern 4.7 4.1 4.8 3.5 3.9 5.0 5.1 4.4 Western 4.1 5.8 4.9 4.3 4.3 6.4 5.5 3.4 Source: U.S. Bureau of Labor Statistics Display these rates as two dotplots using the same scale; compare means and
[EX03-008] Consider the accompanying contingency table, which presents the results of an advertising survey about the use of credit by Martan Oil Company customers.Number of Purchases at Gasoline Station Last Year Preferred Method of Payment 0–4 5–9 10–14 15–19 20 Sum Cash 150 100 25 0 0
[EX03-007] 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:Television Station Political Affiliation ABC CBS NBC PBS FOX
[EX03-006] Under the National Highway System Designation Act of 1995, states are allowed to set their own highway speed limits. Most of the states raised the limits. The 2005 maximum speed limits on interstate highways for cars and trucks by each state are given in the following table (in miles per
3.3 [EX03-003] In a national survey of 500 business and 500 leisure travelers, each was asked where they would most like “more space.”On Airplane Hotel Room All Other Business 355 95 50 Leisure 250 165 85a. Express the table as percentages of the total.b. Express the table as percentages of the
a. Is there 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? Do
[EX03-001] Refer to the 2003–2004 Timberwolves data on page 145 to answer the following questions:a. Is there a relationship (pattern) between the two variables, points scored per game and number of personal fouls committed per game?Explain why or why not.b. Do you think it is reasonable (or
Student A stated, “Both the standard deviation and the variance preserve the same unit of measurement as the data.” Student B disagreed, arguing, “The unit of measurement for variance is a meaningless unit of measurement.”Who is right? Justify your answer.
A set of test papers was machine scored.Later it was discovered that 2 points should be added to each score. Student A said, “The mean score should also be increased by 2 points.” Student B added, “The standard deviation should also be increased by 2 points.”Who is right? Justify your
Create a set of data containing three or more values in the following cases:a. Where the mean is 12 and the standard deviation is 0b. Where the mean is 20 and the range is 10c. Where the mean, median, and mode are all equald. Where the mean, median, and mode are all differente. Where the mean,
Mr. VanCott started his own machine shop several years ago. His business has grown and become very successful in recent years.Currently he employs 14 people, including himself, and pays the following annual salaries:Owner, President $80,000 Worker $25,000 Business Manager 50,000 Worker 25,000
The Corner Convenience Store kept track of the number of paying customers it had during the noon hour each day for 100 days.The resulting statistics are rounded to the nearest integer:mean 95 midrange 93 median 97 range 56 mode 98 standard first quartile 85 deviation 12 third quartile
a. Find the standard score for the value x 452 relative to its sample, where the sample mean is 500 and the standard deviation is 32.b. Find the value of x that corresponds to the standard score of 1.2, where the mean is 135 and the standard deviation is 15.
Given the set of data 4, 8, 9, 8, 6, 5, 7, 5, 8, find each of the following sample statistics:a. Meanb. Medianc. Moded. Midrangee. First quartilef. P40 g. Variance h. Standard deviation i. Range
A sample of the purchases of several Corner Convenience Store customers resulted in the following sample data (x number of items purchased per customer):x 1 2 3 4 5 f 6 10 9 8 7a. What does the 2 represent?b. What does the 9 represent?c. How many customers were used to form this sample?d. How
a. Design your own study of Internet usage.Define a specific population that you will sample, describe your sampling plan, collect your data, and answer parts c through l in “Putting Chapter 2 to Work,” Exercise 2.224.b. Discuss the differences and similarities between the Internet usage
[EX02-001] Students in a statistics course offered over the Internet were asked how many different Internet activities they engaged in during a typical week. The following data show the number of activities:6 7 3 6 9 10 8 9 9 6 4 9 4 9 4 2 3 5 13 12 4 6 4 9 5 6 9 11 5 6 5 3 7 9 6 5 12 2 6 9a. List
[EX02-223] The earnings per share for 40 firms in the radio and transmitting equipment industry follow:4.62 0.10 1.29 7.25 6.04 3.20 9.56 4.90 4.22 3.71 0.25 1.34 2.11 5.39 0.84 0.19 3.72 2.27 2.08 1.12 1.07 2.50 2.14 3.46 1.91 7.05 5.10 1.80 0.91 0.50 5.56 1.62 1.36 1.93 2.05 2.75 3.58 0.44 3.15
Do your monthly car payments prevent you from spending money on other things? More than 56% say, “yes.” The distribution of the amount spent on monthly car payments is as follows: 32%spend less than $300, 43% spend $300 to $499, 17% spend $500 to $699, and 8% spend $700 or more. Suppose that
[EX02-221] The lifetimes of 220 incandescent 60-watt lamps were obtained and yielded the frequency distribution shown in this table:Class Limits f Class Limits f 500–600 3 1000–1100 57 600–700 7 1100–1200 23 700–800 14 1200–1300 13 800–900 28 1300–1400 7 900–1000 64 1400–1500

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