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elementary statistics

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

A computer was used to complete the preliminary calculations: form the extensions table; calculate the summations x, y, x2, xy,y2; and find the SS(x), SS(y), and SS(xy) for the following set of bivariate data. Verify the results by calculating the values yourself. X 45 52 49 60 67 y 22 26 21 28 33
National Football League (NFL)football enthusiasts often look at a team’s total points scored for (Pts F) and total points scored against (Pts A) as a way of comparing the relative strength of teams. The season totals for the 32 teams in the NFL 2004 season are shown here.a. Calculate the linear
[EX13-12] Knowing a horse’s weight(measured in pounds) is important information for a horse owner. The amount of feed and medicine dosages all depend on the horse’s weight. Most owners do not have the resources to have a scale large enough to weigh a horse, so other measurements are used to
a. Calculate the covariance of the set of data (20, 10), (30, 50), (60, 30), (80, 20), (110, 60), and (120, 10).b. Calculate the standard deviation of the six x-values and the standard deviation of the six y-values.c. Calculate r, the coefficient of linear correlation, for the data in part a.d.
Using graphs to illustrate, explain the meaning of a correlation coefficient with the following values:a. 1.0b. 0.0c. 1.0d. 0.5e. 0.6 13.16 Using Figure 13.5 on page 705, find the 95% interval when a sample of n 25 results in r 0.35.
a. Using Figure 13.5 on page 705, find the 95% interval when a sample of n 100 results in r 0.35.b. Compare your answer in part a with the confidence interval formed in Exercise 13.16. Describe what occurred when you increased the sample size.
Does a country’s gross domestic product (GDP) indicate its level of technology? The 2005 Edition of The EU-15’s New Economy—A Statistical Portrait provided statistics on its European Union members. The following information was obtained for a random sample of five of the countries.Find r and
The test–retest method is one way of establishing the reliability of a test. The test is administered, and then, at a later date, the same test is readministered to the same individuals. The correlation coefficient is computed between the two sets or scores. The following test scores were
Perhaps the size of an animal’s brain determines intelligence for that species. Or perhaps the weight of the brain. Or perhaps their body size or weight have a role. The following chart compares several animals’ brain and body sizes and weights.Calculate the correlation coefficient and use it
Portugal is known for its sweet port, or “simple rose.” To keep with the current trend of dry table wines, Portuguese winemakers are adding new reds to their inventory of wines.Listed in the table are five varieties with their Wine Spectator score and price per bottle. Wine Spectator rates
A new study shows that the death rate on rural roads is higher than that on other roads in the United States. The table that follows is an excerpt taken from “Death rates higher on rural road” in the March 3, 2005, USA Today, which gives the death rates for each state on rural, noninterstate
Determine the bounds on the p-value that would be used in testing each of the following null hypotheses using the p-value approach:a. Ho: 0 vs. Ha: 0, with n 32 and r 0.41b. Ho: 0 vs. Ha: 0, with n 9 and r 0.75c. Ho: 0 vs. Ha: 0, with n 15 and r 0.83
Determine the critical values that would be used in testing each of the following null hypotheses using the classical approach.a. Ho: 0 vs. Ha: 0, with n 18 and 0.05b. Ho: 0 vs. Ha: 0, with n 32 and 0.01c. Ho: 0 vs. Ha: 0, with n 16 and 0.05
13.35 When it comes to high-end Japanese eateries featuring sushi, the quality and presentation of the food are no doubt indicators of the cost. What about the décor of the restaurant? Would that also have an effect on the cost? Zagat Survey results, published in the November 11, 2004, Newsweek,
13.36 Is a value of r 0.24 significant in trying to show that is greater than zero for a sample of size 62 at the 0.05 level of significance?
13.37 [EX13-37] The population (in millions) and the violent crime rate (per 1000) were recorded for 10 metropolitan areas. The data are shown in the following table.Population 10.0 1.3 2.1 7.0 4.4 0.3 0.3 0.2 0.2 0.4 Crime Rate 12.0 9.5 9.2 8.4 8.2 7.3 7.1 7.0 6.9 6.9 Do these data provide
13.38 [EX13-38] One would think that playing in the National Basketball Association (NBA) regular season, competing at the 2004 Olympics, and then playing in the NBA postseason would tire any player out. A look at six former Olympians still playing in the postseason gives a different impression, as
13.39 [EX13-39] Two indicators of the level of economic activity in a given geographical area are its total personal income and the value of new privately owned housing units. The following table lists the data for seven states for the year 2004.a. Calculate the correlation coefficient between the
13.40 [EX13-40] Sugar beet growers are interested in realizing higher yields and higher sucrose percentages from their crops. But do they go together?The data that follow are from the Montana 2003 sugar beet crop—values listed are by county, yield is tons per acre, and sucrose is percentage of
13.41 [EX13-41] Ten salespeople were surveyed, and the average number of client contacts per month, x, and the sales volume, y (in thousands), were recorded for each:.Refer to the following computer output and verify that the equation of the line of best fit is ˆ y 13.4 2.3x and that se 10.17
13.42 [EX13-42] Nationwide, hailstones cause about $1 billion in property and crop damage each year, according to the April 25, 2005, USA Today Weather Focus report “Violent storms create the largest hail.” The speed of a thunderstorm’s updraft is one of the factors affecting the size
13.43 [EX13-43] The NBA calculates many statistics, just like all other professional sports. Average points per game, average rebounds per game, number of years played, number of titles, number of All-Star appearances, and number of most valuable player (MVP) awards are just some examples that were
Thirteen of Minnesota’s sweet corn–producing counties were randomly selected, and the following information about their 2004 crop was recorded: acres planted (100s of acres)and total production in 100s of tons of sweet corn.a. Investigate the relationship between the number of acres planted to
Diamonds are often thought of as a cherished item with a personal value well in excess of their monetary value. The monetary value of a diamond is determined by its exact quality as defined by the 4 Cs: cut, color, clarity, and carat weight. The price (dollars) and the carat weight of a diamond are
a. Using the 10 points shown in the following table, find the equation of the line of best fit, y^ b0 b1x and graph it on a scatter diagram.b. Find the ordinates y^ for the points on the line of best fit whose abscissas are x 1, 3, 5, 7, and 9.c. Find the value of e for each of the points in the
a. The vertical scale in the figure in Applied Example 13.7 on page 720 is drawn at At 12,600, and the line of best fit appears to intersect the vertical scale at approximately 35,500. Verify the coordinates of this point of intersection.b. The article also gives an interval estimate of (3.001,
Calculate the estimated standard error of regression, sb1, for the computer-science aptitude score–achievement score relationship in Exercise 13.46 (p. 718).
Calculate the estimated standard error of regression, sb1, for the number of hours studied–exam grade relationship in Exercise 13.48 (p. 718).
Using the estimated standard error of regression, sb1, found in Exercise 13.51 for the number of hours studied–exam grade relationship, find the 95% confidence interval for the population slope 1. The equation for the line of best fit was:ˆy 3.96 0.625x.
Determine the p-value for each of the following situations.a. Ha:1 0, with n 18 and t 2.4b. Ha:1 0, with n 15, b1 0.16, and sb1 0.08c. Ha:1 0, with n 24, b1 1.29, and sb1 0.82
Determine the critical value(s) and regions that would be used in testing each of the following null hypotheses using the classical approach:a. Ho:1 0 vs. Ha:1 0, with n 18 and 0.05b. Ho:1 0 vs. Ha:1 0, with n 28 and 0.01c. Ho:1 0 vs. Ha:1 0, with n 16 and 0.05
An issue of Popular Mechanics gives specifications and dimensions for various jet boats. The following table summarizes some of this information.Model Base Price Engine Horsepower Baja Blast $8,395 120 Bayliner Jazz $8,495 90 Boston Whaler Rage 15 $11,495 115 Dynasty Jet Storm $8,495 90 Four Winds
Each student in a sample of 10 was asked for the distance and the time required to commute to college yesterday. The data collected are shown in the table on p. 726.a. Draw a scatter diagram of these data.b. Find the equation that describes the regression line for these data.c. Does the value of b1
13.60 [EX13-60] Diopters represent the amount of correction needed to provide 20/20, or normal, vision. The greater the degree of nearsighted or farsighted vision, the higher the corrective prescription in diopters. Measurements in negative diopters refer to nearsighted vision, whereas measurements
13.61 [EX13-61] The company in Exercise 13.60 must also look at other competitive lenses. It obtains another sample of 30 lenses from a lot shipped for comparison. It labeled these lenses as Group 2. Acceptance of this lot also depended on the relationship between the lens power and the optical
13.62a. Compare and contrast the two samples of lenses in Exercises 13.60 and 13.61.Include comparative descriptions of the data, the correlation analyses, and the regression analyses.b. Identify one specific noticeable difference between these two samples.
13.63 A study in Physical Therapy reports on seven different methods to determine crutch length plus two new techniques using linear regression. One of the regression techniques uses the patient’s reported height. The study included 107 individuals.The mean of the self-reported heights was 68.84
13.64 [EX13-64] Cicadas are flying, plant-eating insects. One particular species, the 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
13.65 Use the data and the answers found in Exercise 13.59 (p. 725) to make the following estimates.a. Give a point estimate for the mean time required to commute 4 miles.b. Give a 90% confidence interval for the mean travel time required to commute 4 miles.c. Give a 90% prediction interval for the
Refer to Applied Example 13.11 on page 733. The graphs for Site S-25 and Site S-27 display 95% confidence intervals of the regression line.What distinguishing feature would 95% prediction intervals have with respect to these graphs? Explain the difference between confidence intervals and prediction
The relationship between the“strength” and “fineness” of cotton fibers was the subject of a study that produced the following data.a. Draw a scatter diagram.b. Find the 99% confidence interval for the mean measurement of fineness for fibers with a strength of 80.c. Find the 99% prediction
Mr. B, the manager at a large retail store, is investigating several variables while measuring the level of his business. His store is open every day during the year except for New Year’s Day, Christmas, and all Sundays. From his records, which cover several years prior, Mr. B has randomly
Mr. B, store manager in Exercise 13.69 (and Exercises 12.36–12.38), found the data from the months of November and December to be different from the data for the other months. Since the data that is separate from the rest in the scatter diagram in Exercise 13.69 is from November and December,
Help Mr. B, the store manager in Exercises 13.69 and 13.70 (and Exercises 12.36–12.38), by analyzing the relationship between the numbers of items purchased daily and the total daily sales for the data from the first 10 months of the year.a. Construct the scatter diagram for the data for January
Do you think your height and shoe size are related? Probably so. There is a known “quick” relationship that says your height(in inches) can be approximated by doubling your shoe size and adding 50 (y 2x 50). A random sample of 30 community college students’ heights and shoe sizes was
Explain why a 95% confidence interval for the mean value of y at a particular x is much narrower than a 95% prediction interval for an individual y value at the same value of x.
When x0 x, is the formula for the standard error of y^x0 what you might have expected it to be, s ? Explain.
About 2527 athletes competed in the 2002 Olympic Winter Games held at Salt Lake City, Utah, with medals in 78 events. Athletes from 78 nations and territories participated. The following table shows the distribution of gold, silver, and bronze medals awarded to athletes representing the 18 nations
A study in the Journal of Range Management examines the relationships between elements in Russian wild rye. The correlation coefficient between magnesium and calcium was reported to be 0.69 for a sample of size 45. Is there a significant correlation between magnesium and calcium in Russian wild rye
An article in Geology gives the following equation relating pressure, P, and total aluminum content, AL, for 12 Horn blende rims:P 3.46(0.24) 4.23(0.13)AL. The quantities shown in parentheses are standard errors for the y-intercept and slope estimates. Find a 95%confidence interval for the
The tobacco settlement negotiated by a team of eight attorneys general on behalf of 41 states resulted in $206 billion to be paid by the tobacco industry to recoup Medicaid costs the states incurred while treating ill smokers. Payments are to be made in annual increments over a 25-year span from
The following set of 25 scores was randomly selected from a teacher’s class list.Let x be the prefinal average and y be the final examination score. (The final examination had a maximum of 75 points.)Student x y 1 75 64 2 86 65••• Remainder of data on Student’s Suite CD-ROM.a. Draw a
[EX13-85] It is believed that the amount of nitrogen fertilizer used per acre has a direct effect on the amount of wheat produced. The following data show the amount of nitrogen fertilizer used per test plot and the amount of wheat harvested per test plot.x, Pounds of Fertilizer y, 100 Pounds of
[EX13-70] Help Mr. B, the store manager in Exercises 13.69–13.71 (and Exercises 12.36–12.38), by analyzing the relationship between the number of customers per day and the total daily sales for the data from the first 10 months of the year.a. Use your calculator or computer to construct the
Compare the results obtained in Exercises 13.70, 13.71, and 13.86. Explain the similarities and differences. Why do you think the scatter diagram for number of items purchased and total sales shows less variability about the line of best fit than do the other two scatter diagrams?
[EX13-70] Investigate the relationship of the variables studied in Exercises 13.69, 13.70, 13.71, 13.86, and 13.87 for the November and December data.November & December Day N&D Month N&D Customers N&D Items N&D Sales N&D 6 11 1049 3799 40,362.70••• Remainder of data on Student’s Suite
The correlation coefficient, r, is related to the slope of best fit, b1, by the equation r b1 Verify this equation using the following data.x 1 2 3 4 6 y 4 6 7 9 12
The following equation is known to be true for any set of data: (y y)2 (y y^)2 (y^ y)2.Verify this equation with the following data.
13.91 [EX13-01] Refer to the wheat crop data in Section 13.1 on page 696.a. Construct a scatter diagram and find the linear correlation coefficient and the equation for the line of best fit for Planted (x) and Production(y).b. Find the 95% confidence interval for the true linear correlation
Design your own study to investigate another grain. Answer questions similar to those asked in Exercise 13.91. Use the Internet and the U.S. Department of Agriculture’s National Agricultural Statistics Service website (http://www.usda.gov/nass/) to find your data. The data sets posted will
13.1 The error must be normally distributed if inferences are to be made. True/False
13.2 Both x and y must be normally distributed. True/False
13.3 A high correlation between x and y proves that x causes y. True/False
13.4 The value of the input variable must be randomly selected to achieve valid results. True/False
13.5 The output variable must be normally distributed about the regression line for each value of x. True/False
13.6 Covariance measures the strength of the linear relationship and is a standardized measure. True/False
13.7 The sum of squares for error is the name given to the numerator of the formula used to calculate the variance of y about the line of regression. True/False
13.8 Correlation analysis attempts to find the equation of the line of best fit for two variables. True/False
13.9 There are n 3 degrees of freedom involved with the inferences about the regression line. True/False
13.10 ˆy serves as the point estimate for bothy|x0 and yx0. True/False
13.11 Draw a scatter diagram of the data. Be sure to label completely. It is believed that the amount of nitrogen fertil- izer used per acre has a direct effect on the amount of wheat produced. The following data show the amount of nitrogen fertilizer used per test plot and the amount of wheat
13.12 Complete an extensions table. It is believed that the amount of nitrogen fertil- izer used per acre has a direct effect on the amount of wheat produced. The following data show the amount of nitrogen fertilizer used per test plot and the amount of wheat harvested per test plot. All test plots
13.13 Calculate SS(x), SS(xy), and SS(y). It is believed that the amount of nitrogen fertil- izer used per acre has a direct effect on the amount of wheat produced. The following data show the amount of nitrogen fertilizer used per test plot and the amount of wheat harvested per test plot. All test
13.14 Calculate the linear correlation coefficient, r. It is believed that the amount of nitrogen fertil- izer used per acre has a direct effect on the amount of wheat produced. The following data show the amount of nitrogen fertilizer used per test plot and the amount of wheat harvested per test
13.15 Determine the 95% confidence interval estimate for the population linear correlation coefficient. It is believed that the amount of nitrogen fertil- izer used per acre has a direct effect on the amount of wheat produced. The following data show the amount of nitrogen fertilizer used per test
13.16 Calculate the equation of the line of best fit. It is believed that the amount of nitrogen fertil- izer used per acre has a direct effect on the amount of wheat produced. The following data show the amount of nitrogen fertilizer used per test plot and the amount of wheat harvested per test
13.17 Draw the line of best fit on the scatter diagram. It is believed that the amount of nitrogen fertil- izer used per acre has a direct effect on the amount of wheat produced. The following data show the amount of nitrogen fertilizer used per test plot and the amount of wheat harvested per test
13.18 Calculate the standard deviation of the y values about the line of best fit. It is believed that the amount of nitrogen fertil- izer used per acre has a direct effect on the amount of wheat produced. The following data show the amount of nitrogen fertilizer used per test plot and the amount
13.19 Does the value of b1 show strength significant enough to conclude that the slope is greater than zero at the 0.05 level? It is believed that the amount of nitrogen fertil- izer used per acre has a direct effect on the amount of wheat produced. The following data show the amount of nitrogen
13.20 Determine the 0.95 confidence interval for the mean yield when 85 lb of fertilizer are used per plot. It is believed that the amount of nitrogen fertil- izer used per acre has a direct effect on the amount of wheat produced. The following data show the amount of nitrogen fertilizer used per
13.21 Draw a line on the scatter diagram representing the 95% confidence interval found in question 13.20. It is believed that the amount of nitrogen fertil- izer used per acre has a direct effect on the amount of wheat produced. The following data show the amount of nitrogen fertilizer used per
13.22 “There is a high correlation between how frequently skiers have their bindings tested and the incidence of lower-leg injuries, according to researchers at the Rochester Institute of Technology. To make sure your bindings release properly when you begin to fall, you should have them serviced
13.23 If a “moment” is defined as the distance from the mean, describe why the method used to define the correlation coefficient is referred to as “a product moment.”
13.24 If you know that the value of r is very close to zero, what value would you anticipate for b1? Explain why.
13.25 Describe why the method used to find the line of best fit is referred to as “the method of least squares.”
13.26 You wish to study the relationship between the amount of sugar in a child’s breakfast and the child’s hyperactivity in school during the 4 hours after breakfast.You ask 200 mothers of fifth-grade children to keep a careful record of what the children eat and drink each morning. Each
13.27 You are interested in studying the relationship between the length of time a person has been supported by welfare and self-esteem. You believe that the longer a person is supported, the lower the selfesteem.What data would you need to collect and what statistics would you calculate if you
14.4 [EX14-04] Ten randomly selected shut-ins were each asked how many hours of television they watched last week. The results are as follows:82 66 90 84 75 88 80 94 110 91 Determine the 90% confidence interval estimate for the median number of hours of television watched per week by shut-ins.
14.5 [EX14-05] The following daily high temperatures(°F) were recorded in the city of Rochester, New York, on 20 randomly selected days in December.47 46 40 40 46 35 34 59 54 33 65 39 48 47 46 46 42 36 45 38 Use the sign test to determine the 95% confidence interval for the median daily high
14.6 [EX14-06] Fifteen peanut-producing counties were randomly identified, and the 2004 peanut yield rate, in pounds of peanuts harvested per acre, was recorded.3755 2885 3080 3200 3035 3365 2850 3850 3455 3015 3310 2915 3630 3765 3050 Source: http://www.nass.usda.gov:81/ipedbcnty/report2.htm Use
14.7 [EX14-07] Every year sixth-grade students in Ohio schools take proficiency tests. The following list is of sixth-grade reading score changes from the prior year. Negative values indicate a decrease in score, positive values show an increase, and a zero shows no change from the prior
14.8 [EX14-08] A sample of the daily rental-car rates for a compact car was collected in order to estimate the average daily cost of renting a compact car.Find the 99% confidence interval for the median daily rental cost. 39.93 41.00 42.99 38.99 42.93 35.00 40.95 29.99 49.93 50.95 34.95 28.99 43.93
14.11 Determine the p-value for the following hypothesis tests involving the sign test:a. Ho: P() 0.5 vs. Ha: P() 0.5, with n 18 and x n() 3b. Ho: P() 0.5 vs. Ha: P() 0.5, with n 78 and x n() 30c. Ho: P() 0.5 vs. Ha: P() 0.5, with n 38 and x n() 10d. Ho:
14.12 Determine the critical value that would be used to test the null hypothesis for the following situations using the classical approach and the sign test:a. Ho: P() 0.5 vs. Ha: P() 0.5, with n 18 and 0.05b. Ho: P() 0.5 vs. Ha: P() 0.5, with n 78 and 0.05c. Ho: P() 0.5
14.13 An article titled “Graft-versus-Host Disease”(http://www.nature.com/bmt/journal/v35/n10/abs/1704957a.html) gives the median age of 42 years for the 87 patients with acute myeloid leukemia (AML) who received hematopoietic stem cell transplants from unrelated donors after standard
14.14 [EX14-07] Every year sixth-grade students in Ohio schools take proficiency tests. The list of sixth-grade reading score changes from the prior year are given in Exercise 14.7. Negative values indicate a decrease in score, positive values show an increase, and a zero shows no change from the
14.15 According to the June 13, 2005, USA Today Weather Focus article “Teen girls more careful in the sun,” 48% of teen boys say they wear protective clothing to combat the sun’s danger versus 52% of the teen girls. Suppose we wish to test the null hypothesis that one-half of all teen boys
14.16 [EX14-16] In “The Annual Report on the Economic Status of the Profession” done by American Association of University Professors, the mean salary of a full professor was reported to be$83,282. The following table lists the average salary (in dollars) for a random sample of institutions in
14.17 [EX14-17] Part of the results from the Third International Mathematics and Science Study was a comparison of eighth-grade science achievement by nation from 1995, 1999, and 2003. The following table gives the average scores for the nations with all three years.a. Construct a table showing the
14.19 A blind taste test was used to determine people’s preference for the taste of the “classic”cola and “new” cola. The results were as follows:645 preferred the new 583 preferred the old 272 had no preference Is the preference for the taste of the new cola significantly greater than

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