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elementary statistics

Questions and Answers of Elementary Statistics

[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
[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
[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
[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
[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:
[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
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
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
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
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
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
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
[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
[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
[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
[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 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
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
[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
[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
[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
[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
[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
[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
[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
[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
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)
[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
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
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
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
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
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
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
[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
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
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
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
[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
[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
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
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
[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
[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
[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
[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
[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,
[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
[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
[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
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
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
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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
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
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
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
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
[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
[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
[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
[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.
[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
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
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
[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
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
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
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,
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
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
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
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
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
[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
[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
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
[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

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