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Elementary Statistics 11th Edition Robert R. Johnson, Patricia J. Kuby - Solutions

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€™s 2009 season are shown below:a. Calculate the linear
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
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.
A formula that is sometimes given for computing the correlation coefficient is
Using graphs to illustrate, explain the meaning of a correlation coefficient with the following values: a. - 1.0 b. 0.0 c. +1.0 d. _0.5 e. _0.6
Use Table 10 of Appendix B to determine a 95% confidence interval for the true population linear correlation coefficient based on the following sample statistics: a. n = 8 r = 0.20 b. n = 100 r = - 0.40 c. n = 25, r = - 0.65 d. n = 15, r = - 0.23
Use Table 10 of Appendix B to determine a 95% confidence interval for the true population linear correlation coefficient based on the following sample statistics: a. n = 50 r = 0.60 b. n = 12 r = - 0.45 c. n = 6 r = + 0.80 d. n = 200 r = - 0.56
Consider the “Married Couples’ Heights” scatter diagram presented in “Height Compatibility” on page 612: a. How can a husband and wife of the same height be located on the given scatter diagram? How many were there? (Determine this answer in two ways: 1—count the points on the scatter
Does a country€™s gross domestic product (GDP) indicate its level of technology? The CIA World Factbook [https://www.cia.gov/] provides statistics on all world countries. The following 2008 information was obtained for a random sample of five countries:Find r and set a 95% confidence
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 of scores. The following test scores
Perhaps the size of an animal€™s brain determines intelligence for that species. Or perhaps the weight of the brain does. Or perhaps body size or weight has a role.The following chart compares several animals€™ brain and body sizes and weights.Calculate the correlation
California is noted for its dry Chardonnay wines. Listed in the table are five varieties, with their Wine Spectator score and price per bottle. Wine Spectator rates wines on a 100-point scale, and all wines are blind-tasted.a. Calculate r. b. Set a 95% confidence interval of r. c. Describe the
A 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 €œDeath rates higher on rural road€ in USA Today, which gives the death rates for each state on rural, noninterstate roads
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following statements: a. The linear correlation coefficient is positive. b. There is no linear correlation. c. There is evidence of negative correlation. d. There is a positive linear relationship.
a. State the standard null hypothesis, Ho, for testing the linear correlation coefficient, p. b. What does a decision of “Fail to reject Ho” indicate in a hypothesis test for p? c. What does a decision of “Reject Ho” indicate in a hypothesis test for p?
Place bounds on the p-value resulting from a sample With n = 18 and r = 0.444 in the following circumstances: a. Ha is two-tailed. b. Ha is one-tailed.
Determine the bounds on the p-value that would be used in testing each of the following null hypotheses using the p-value approach:
Determine the critical values of r for a = 0.05 and n = 20 in the following circumstances: a. Ha is two-tailed. b. Ha is one-tailed.
Consider a set of paired bivariate data. a. Explain why ∑(x = x) = 0 and ∑(y = y) = 0 b. Describe the effect that lines x = and y = have on the graph of these points. c. Describe the relationship of the ordered pairs that will cause g[(x = ) • (y = ) to be (1) positive, (2) negative,
Determine the critical values that would be used in testing each of the following null hypotheses using the classical approach.
Referring to Applied Example 13. 4: a. Explain the meaning of “Correlation coefficient for these data was 0.58 (linear p = 0.008 s reported for Phase 2. b. Using Table 11, what bounds would be placed on the p-value? How do these bounds compare with the p-value in part a? c. What is the critical
a. If a sample of size 10 has a linear correlation coefficient of 0.60, is there significant reason to conclude that the linear correlation coefficient of the population is positive? Usea = 0.01 . b. If a sample of size 42 has a linear correlation coefficient of 0.60, is there significant reason to
A sample of 20 bivariate data has a linear correlation coefficient of r = 0.43 Does this provide sufficient evidence to reject the null hypothesis that p = 0 in favor of a two-sided alternative? Use a = 0.10.
If a sample of size 18 has a linear correlation coefficient of _0.50 is there significant reason to conclude that the linear correlation coefficient of the population is negative? Use a = 0.01
Is a value of r__0.24 significant in trying to show that r is greater than zero for a sample of size 62 at the 0.05 level of significance?
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 Newsweek, produced a correlation
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.
One would think that playing in the Olympics and then the NBA regular season and postseason would tire any player out. Do the scoring averages of these nine 2008 Olympians who also played in the postseason give that impression?a. Do these data provide evidence to reject the null hypothesis that p =
Two indicators of the level of economic activity in a given geographical area are its median household income and its percent of population in poverty. The table below lists the data for seven states for the year 2008:a. Calculate the correlation coefficient between the two variables. b. Test for a
Consider the “Married Couples’ Heights” scatter diagram presented in “Height Compatibility” on page 613: a. Calculate r. b. Set a 95% confidence interval for r. c. Test for a significant positive correlation at the 0.05 level of significance. d. Explain the meaning of the results found in
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 sugar beet crop€”values listed are by county, yield is tons per acre, and sucrose is percentage of sucrose.
The graphic in Applied Example 13. 6 reports the effect each at-fault traffic accident had on 2009 average annual auto insurance premiums. a. Does it appear that the variable “number of at-fault accidents” had a recurring effect on average annual premiums? Estimate the annual effect. b. How
The National Basketball Association calculates many statistics, just like any other professional sport. Average points per game, average rebounds per game, number of years played, number of titles, number of All-Star appearances, and number of MVP awards are just some examples. Using the data
Thirteen of Minnesota€™s sweet corn€“producing counties were randomly selected, and the following information about their crop was recorded: acres planted (in 100s of acres) and total production in 100s of tons of sweet corn.Source: www.nass.usda.gov a. Investigate the
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 C’s: cut, color, clarity, and carat weight. The price (dollars) and the carat weight of a diamond
The computer science aptitude score, x, and the achievement score, y (measured by a comprehensive final), were measured for 20 students in a beginning computer science course. The results were as follows. Find the equation of the line of best fit and s2e
a. Using the 10 points shown in the following table, find the equation of the line of best fit, yË† = b0 = b1x and graph it on a scatter diagram.b. Find the ordinates 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
The following data values are from a random sample of 40 college students; the data show the students€™ gender, American College Test (ACT) composite scores, and grade point averages (GPAs) after their first term in college.a. Construct a scatter diagram of the data with ACT scores on the
The following data show the number of hours studied for an exam, x, and the grade received on the exam, y (y is measured in 10s; that is y = 8, means that the grade, rounded to the nearest 10 points, is 80).a. Draw a scatter diagram of the data. b. Find the equation of the line of best fit and
a. The vertical scale in the figure in Applied Example 13. 8 on page 636 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, , for the computer science aptitude score–achievement score relationship in Exercise 13. 48
Calculate the estimated standard error of regression, sb1 for the number of hours studied–exam grade relationship in Exercise 13. 50 .
Using the estimated standard error of regression, sb1 found in Exercise 13. 53 for the number of hours studied–exam grade relationship, find the 95% confidence interval for the population slope b1. The equation for the line of best fit was: yˆ = 3.96 + 0.625x yˆ = 3.96 = 0.625x
Does the time spent watching television take over a young person€™s reading time? A quick random survey of seventh grade girls provided the following results.Let Y be the number of books read in the last year and X be the time spent watching television each week night. a. Find the
Interstate 90 is the longest of the east€“west U.S. interstate highways, with its 3112 miles stretching from Boston, MA,at I-93 on the eastern end to Seattle, WA, at the Kingdome on the western end. It travels across 13 northern states; the number of miles and number of intersections in
An article titled €œStatistical Approach for the Estimation of Strontium Distribution Coefficient€ (Environmental Science & Technology) reports a linear correlation coefficient of 0.55 between the strontium distribution coefficient (mL/g) and the total aluminum (mmol/100
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following statements: a. The slope for the line of best fit is positive. b. The slope of the regression line is not significant. c. The negative slope for the regression is significant.
Determine the p-value for each of the following situations.
Aerial photographs are one of many techniques used to monitor wildlife populations. Knowing the number of animals and their locations relative to areas inhabited by the human population is very useful. It is also important to monitor physical characteristics of the animals. Is it possible to use
Determine the critical value(s) and regions that would be used in testing each of the following null hypotheses using the classical approach:
An issue of Popular Mechanics gives specifications and dimensions for various jet boats. The following table summarizes some of this information.Using the Excel output at the bottom of the page: Using the Excel output at the bottom of the page: a. Determine the equation for the line of best fit. b.
€œThe fast food hamburger remains the single largest seller in fast food restaurants in America€ according to the www.loseweightgroup.com/ website. McDonald€™s, Burger King, etc., are all required to provide nutritional facts about their various burgers. Do the
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 here.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 show sufficient
The relationship between the diameter of a spot weld, x, and the shear strength of the weld, y, is very useful. The diameter of the spot weld can be measured after the weld is completed. The shear strength of the weld can be measured only by applying force to the weld until it breaks. Thus, it
Consider the “Married Couples’ Heights” scatter diagram presented in “Height Compatibility” on page 612: a. Find the equation for the line of best fit. b. Is the value of b1 significantly greater than zero at the 0.05 level? c. Find the 95% confidence interval for b1.
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 in positive
a. Compare and contrast the two samples of lenses in Exercises 13. 66 and 13. 67. Include comparative descriptions of the data, the correlation analyses, and the regression analyses. b. Identify one specific, noticeable difference between these two samples.
A study in Physical Therapy reports on seven different methods to determine proper 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
a. Construct a scatter diagram of the following bivariate data.b. Calculate the covariance. c. Calculate sx and sy. d. Calculate r using formula (13.2). e. Calculate r using formula (13.3).
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 cicada. The adult body
Use the data and the answers found in Exercise13. 63 (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 travel
An experiment was conducted to study the effect of a new drug in lowering the heart rate in adults. The data collected are shown in the following table.a. Find the 95% confidence interval for the mean heart rate reduction for a dose of 2.00 mg. b. Find the 95% prediction interval for the heart rate
The relationship between the “strength” and “fineness” of cotton fibers was the subject of a study that produced the data below. 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
Use the “Married Couples’ Heights” data and the answers found in Exercise 13. 65 to make the following estimates. a. Give a point estimate for the mean husband height for a wife height of 59 inches. b. Give a 95% confidence interval for the mean husband height for a wife height of 59
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
Mr. B, store manager in Exercise 13. 77 (and Exercises 12.44€“12.46), found the data from the months of November and December to be different from the data for the other months. Since the data that are separate from the rest in the scatter diagram in Exercise13. 77 are from November and
Help Mr. B, the store manager in Exercises 13. 77 and 13. 78 (and Exercises 12.44–12.46), by analyzing the relationship between the numbers of items purchased daily and the total daily sales in the data from the first 10 months of the year. a. Construct the scatter diagram for the data for
a. Draw a scatter diagram of the following bivariate datab. Calculate the covariance. c. Calculate sx and sy. d. Calculate r using formula (13.2). e. Calculate r using formula (13.3).
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
Answer the following as “sometimes,” “always,” or “never.” Explain each “never” and “sometimes” response. a. The correlation coefficient has the same sign as the slope of the least squares line fitted to the same data. b. A correlation coefficient of 0.99 indicates a strong
About 11,028 athletes competed in the 2008 Summer Olympic Games held in Beijing, China, for medals in over 300 events. Athletes from 204 nations and territories participated. The table below shows the distribution of gold, silver, and bronze medals awarded to athletes representing the 20 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
A study concerning the plasma concentration of the drug ranitidine was reported in the Journal of Pharmaceutical Sciences. The drug was administered (coded I), and the plasma concentration of ranitidine was followed for 12 hours. The time to the first peak in concentration was called Tmax1.The same
The use of electrical stimulation (ES) to increase muscular strength is discussed in the Journal of Orthopedic and Sports Physical Therapy. Seventeen healthy volunteers participated in the experiment. Muscular strength, Y, was measured as a torque in foot-pounds, and ES, X, was measured in mA
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 estimate, respectively. Find a 95% confidence
The following data resulted from an experiment performed for the purpose of regression analysis. The input variable, x, was set at five different levels, and observations were made at each level.a. Draw a scatter diagram. b. Draw the regression line by eye. c. Place a star, _, at each level
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 being made in annual increments over a 25-year span from
Twenty-one mature flowers of a particular species were dissected, and the number of stamens and carpels present in each flower were counteda. Is there sufficient evidence to claim a linear relationship between these two variables at a = 0.05 b. What is the relationship between the number of stamens
The following set of 25 scores was randomly selected from a teacher€™s class list. Let x be the pre-final average and y be the final examination score. (The final examination had a maximum of 75 points.)a. Draw a scatter diagram for these data. b. Draw the regression line (by eye) and
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.a. Is there sufficient reason to conclude that the
Help Mr. B, the store manager in Exercises 13. 77–13.79 (and Exercises 12.44–12.46), 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 scatter
Compare the results obtained in Exercises 13. 78, 13.79, and 13. 92. 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?
Investigate the relationship of the variables studied in Exercises 13. 77, 13. 78, 13. 79, 13. 92, and 13. 93 for the November and December data.
The correlation coefficient, r, is related to the slope of best fit, b1, by the equationVerify this equation using the following data.
The following equation is known to be true for any set of data: ˆ‘(y - )2 = ˆ‘ (y - yË†)2 + ˆ‘ (yË† - )2 Verify this equation with the following data.
a. Describe why the sign test may be the easiest test procedure of all to use. b. What population parameter can be tested using the sign test? What property of that parameter allows the sign test to be used? Explain.
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 a = 0.05 b. Ho: P(+) = 0.5 vs. Ha: P(+)0.5, with n = 78 and a = 0.05 c. Ho: P(+) = 0.5 vs.
An article titled “Graft-versus-Host Disease” (www.nature.com/) 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 conditioning. Clinical outcome after the use of two
Every year sixth-grade students in Ohio schools take proficiency tests. The list of sixthgrade reading score changes from the prior year are given in Exercise 14. 5. Negative values indicate a decrease in score, positive values show an increase, and a zero shows no change from the prior year. Use
According to the 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 teen girls. Suppose we wish to test the null hypothesis that one-half of all teen boys wear protective clothing to
Part of the results from the Third International Mathematics and Science Study was a comparison of eighth-grade science achievement by nation in 1999, 2003, and 2007. The table gives the average scores for the nations for all three years.a. Construct a table showing the sign of the difference
An article titled “Naturally Occurring Anticoagulants and Bone Marrow Transplantation: Plasma Protein C Predicts the Development of Venoocclusive Disease of the Liver” (Blood) compared baseline values for antithrombin III with antithrombin II values 7 days after a bone marrow transplant for .45
A blind taste test was used to determine people’s preference for the taste of the “classic” cola and the “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
A taste test was conducted with a regular beef pizza. Each of 133 individuals was given two pieces of pizza, one with a whole-wheat crust and the other with a white crust. Each person was then asked whether he or she preferred the whole-wheat or the white crust. The results were as follows: 65
According to an American Optometric Association survey, 57% of adults wear eyeglasses as their type of corrective lenses. Suppose we wish to test the null hypothesis “One-half of college students wear eyeglasses” as their type of corrective lenses against the alternative that the proportion is
Ten randomly selected shut-ins were each asked how many hours of television they watched last week. The results are as follows:Determine the 90% confidence interval estimate for the median number of hours of television watched per week by shut-ins.
Fifty-one percent of grooms say they want to lose weight before their wedding day, according to the USA Today Snapshot “Weigh-in before the wedding.” Suppose we wish to test the hypothesis that at least one-half of grooms want to lose weight before their wedding. If a random sample of 900
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following statements: a. There is a difference in the distributions of the variable between the two groups of subjects. b. The average value is not the same for both groups. c. The distribution of
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following statements: a. The students in the new reading program scored higher on the comprehension test than the students in the traditional reading programs. b. Men on the grapefruit diet lose more
Determine the p-value that will result when testing the following hypotheses for experiments involving two independent samples: a. Ho: Average(A) = Average(B); Ha: Average(A) > Average(B); with nA = 18, nB = 15, and U = 95 b. Ho: Average(I) = Average(II); Ha: Average(I) ≠ Average(II); with nA =

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