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Introduction To Probability And Statistics 14th Edition William Mendenhall, Robert Beaver, Barbara Beaver - Solutions

Describe the significance of the algebraic sign and the magnitude of r.
What is the difference between deterministic and probabilistic mathematical models?
You are given these data:a. Plot the data points. Based on your graph, what will be the sign of the sample correlation coefficient? b. Calculate r and r2 and interpret their values.
You are given these data:a. Plot the six points on graph paper. b. Calculate the sample coefficient of correlation r and interpret. c. By what percentage was the sum of squares of deviations reduced by using the least squares predictor Å· = a + bx rather than as a predictor of y?
Reverse the slope of the line in Exercise 12.51 by reordering the y observations, as follows:Repeat the steps of Exercise 12.51. Notice the change in the sign of r and the relationship between the values of r2 of Exercise 12.51 and this exercise. In Exercise 12.51 You are given these data: a. Plot
The table gives the numbers of Octolasmis tridens and O. lowei barnacles on each of 10 lobsters.8 Does it appear that the barnacles compete for space on the surface of a lobster?a. If they do compete, do you expect the number x of O. tridens and the number y of O. lowei barnacles to be positively
A social skills training program was implemented with seven mildly challenged students in a study to determine whether the program caused improvement in pre/post measures and behavior ratings. For one such test, the pre- and posttest scores for the seven students are given in the table.9a. What
G. W. Marino investigated the variables related to a hockey player's ability to make a fast start from a stopped position.10 In the experiment, each skater started from a stopped position and attempted to move as rapidly as possible over a 6-meter distance. The correlation coefficient r between a
Refer to Exercise 12.55. Marino calculated the sample correlation coefficient r for the stride rate and the average acceleration rate for the 69 skaters to be .36. Do the data provide sufficient evidence to indicate a correlation between stride rate and average acceleration for the skaters? Use the
Geothermal power is an important source of energy. Since the amount of energy contained in 1 pound of water is a function of its temperature, you might wonder whether water obtained from deeper wells contains more energy per pound. The data in the table are reproduced from an article on geothermal
As much as Americans try to avoid high fat, high calorie foods, the demand for a cold, creamy ice cream cone on a hot day is hard to resist. The popular ice cream franchise Coldstone Creamery posted the nutritional information for its ice cream offerings in three serving sizes-"Like it", "Love it",
Is there any relationship between these two variables? To find out, we randomly selected 12 people from a data set constructed by Allen Shoemaker (Journal of Statistics Education) and recorded their body temperature and heart rate.13a. Find the correlation coefficient r, relating body temperature
You are given five points with these coordinates:a. Use the data entry method on your scientific or graphing calculator to enter the n 5 observations. Find the sums of squares and cross-products, Sxx, Sxy, and Syy. b. Find the least-squares line for the data. c. Plot the five points and graph the
Does a team's batting average depend in any way on the number of home runs hit by the team? The data in the table show the number of team home runs and the overall team batting average for eight selected major league teams for the 2010 season.14a. Plot the points using a scatterplot. Does it appear
An experiment was conducted to observe the effect of an increase in temperature on the potency of an antibiotic. Three 1-ounce portions of the antibiotic were stored for equal lengths of time at each of these temperatures: 30°, 50°, 70°, and 90°. The potency readings observed at
An experiment was conducted to determine the effect of various levels of phosphorus on the inorganic phosphorus levels in a particular plant. The data in the table represent the levels of inorganic phosphorus in micromoles (mmol) per gram dry weight of Sudan grass roots grown in the greenhouse for
An experiment was conducted to investigate the effect of a training program on the time to complete the 100-yard dash. Nine students were placed in the program. The reduction y in time to complete the race was measured for three students at the end of 2 weeks, for three at the end of 4 weeks, and
Some varieties of nematodes, roundworms that live in the soil and feed on the roots of lawn grasses and other plants, can be treated by the application of nematicides. Data collected on the percent kill of nematodes for various rates of application (dosages given in pounds per acre of active
Athletes and others suffering the same type of knee injury often require anterior and posterior ligament reconstruction. In order to determine the proper length of bone grafts, experiments were done using three imaging techniques, and these results were compared to the actual length required. A
Refer to Exercise 12.13 and data set EX1213 regarding the relationship between the Academic Performance Index (API), a measure of school achievement based on the results of the Stanford 9 Achievement test, and the percentage of students who are considered English Learners (EL). The following table
Refer to Exercise 12.14 and data set EX1214 regarding a subject's ability to estimate sizes. The table that follows gives the actual and estimated lengths of the specified objects.a. Use an appropriate program to analyze the relationship between the actual and estimated lengths of the listed
If you play tennis, you know that tennis racquets vary in their physical characteristics. The data in the accompanying table give measures of bending stiffness and twisting stiffness as measured by engineering tests for 12 tennis racquets:a. If a racquet has bending stiffness, is it also likely to
Movement of avocados into the United States from certain areas is prohibited because of the possibility of bringing fruit flies into the country with the avocado shipments. However, certain avocado varieties supposedly are resistant to fruit fly infestation before they soften as a result of
Six points have these coordinates:a. Find the least-squares line for the data. b. Plot the six points and graph the line. Does the line appear to provide a good fit to the data points? c. Use the least-squares line to predict the value of y when x = 3.5. d. Fill in the missing entries in the
Why is it that one person may tend to gain weight, even if he eats no more and exercises no less than a slim friend? Recent studies suggest that the factors that control metabolism may depend on your genetic makeup. One study involved 11 pairs of identical twins fed about 1000 calories per day more
Movie Reviews How many weeks can a movie run and still make a reasonable profit? The data that follow show the number of weeks in release (x) and the gross to date (y) for the top 12 movies during a recent week.17a. Plot the points in a scatterplot. Does it appear that the relationship between x
An agricultural experimenter, investigating the effect of the amount of nitrogen x applied in 100 pounds per acre on the yield of oats y measured in bushels per acre, collected the following data:a. Find the least-squares line for the data. b. Construct the ANOVA table. c. Is there sufficient
A horticulturalist devised a scale to measure the freshness of roses that were packaged and stored for varying periods of time before transplanting. The freshness measurement y and the length of time in days that the rose is packaged and stored before transplanting x are given below.a. Fit a
The Lexus GX is a midsize sport utility vehicle (SUV) sold in North American and Eurasian markets by Lexus. The GX 470 was introduced in 2002 (as a 2003 model) and was later upgraded with a new off-road suspension system. The sales of the Lexus GX 470 from its inception until 2009 are given in the
Six points have these coordinates:a. Find the least-squares line for the data. b. Plot the six points and graph the line. Does the line appear to provide a good fit to the data points? c. Use the least-squares line to predict the value of y when x = 3.5. d. Fill in the missing entries in the MS
Professor Isaac Asimov was one of the most prolific writers of all time. Prior to his death, he wrote nearly 500 books during a 40-year career. In fact, as his career progressed, he became even more productive in terms of the number of books written within a given period of time.1 The data give the
The phrase "made in the U.S.A." has become a familiar battle cry as U.S. workers try to protect their jobs from overseas competition. For the past few decades, a major trade imbalance in the United States has been caused by a flood of imported goods that enter the country and are sold at lower cost
Suppose that E(y) is related to two predictor variables, x1 and x2, by the equation E(y) = 3 + x1 - 2x2 a. Graph the relationship between E(y) and x1 when x2 = 2. Repeat for x2 = 1 and for x2 = 0. b. What relationship do the lines in part a have to one another?
A publisher of college textbooks conducted a study to relate profit per text y to cost of sales x over a 6-year period when its sales force (and sales costs) were growing rapidly. These inflation-adjusted data (in thousands of dollars) were collected:Expecting profit per book to rise and then
Refer to Exercise 13.10.a. Use the values of SSR and Total SS to calculate R2. Compare this value with the value given in the printout.b. Calculate R2(adj). When would it be appropriate to use this value rather than R2 to assess the fit of the model?
Cameras come with many options, and it appears that the more that you want, the higher the cost of the camera. Consumer Reports2 has rated n = 20 cameras on qualities that we consumers are looking for. Variables that may relate to the cost of a camera are given in the following table where y =
Refer to Exercise 13.12. A command in the MINITAB regression menu provides output in which R2 and R2(adj) are calculated for all possible subsets of the five independent variables. The printout is provided here.MINITAB output for Exercise 13.13Best Subsets Regression: y versus x1, x2, x3, x4,
In Exercise 12.77 we presented sales data for the Lexus GX, a mid-size sport utility vehicle (SUV) sold in North American and Eurasian markets by Lexus. The sales of the Lexus GX 470 from its inception until 2009 are given in the table:3a. Plot the data. What model would you expect to provide the
In order to study the relationship of advertising and capital investment with corporate profits, the following data, recorded in units of $100,000, were collected for 10 medium-sized firms in the same year. The variable y represents profit for the year, x1 represents capital investment, and x2
One of the most famous national highways from its beginnings in the 1920s until its demise around 1970 was Route 66. On its way from Chicago to Los Angeles, one of the last stops was San Bernardino, California. Now, a new transportation hub-the San Bernardino International Airport-is in the
Suppose you wish to predict production yield y as a function of several independent predictor variables. Indicate whether each of the following independent variables is qualitative or quantitative. If qualitative, define the appropriate dummy variable(s). a. The prevailing interest rate in the
Suppose E(y) is related to two predictor variables x1 and x2 by the equationE(y) = 3 + x1 - 2x2 + x1x2a. Graph the relationship between E(y) and x1 when x2 = 0. Repeat for x2 = 2 and for x2 = -2.b. Repeat the instructions of part a for the modelE(y) = 3 + x1 - 2x2c. The equation for part a is
A multiple linear regression model involving one qualitative and one quantitative independent variable produced this prediction equation: ŷ = 12.6 + .54x1 - 1.2x1x2 + 3.9x22 a. Which of the two variables is the quantitative variable? Explain. b. If x1 can take only the values 0 or 1, find the two
Refer to Exercise 13.1. a. Graph the relationship between E(y) and x2 when x1 = 0. Repeat for x1 = 1 and for x1 = 2. b. What relationship do the lines in part a have to one another? c. Suppose, in a practical situation, you want to model the relationship between E(y) and two predictor variables x1
One desirable dietary change if you want to "eat right," is to reduce the intake of red meat and to substitute poultry or fish. Researchers tracked beef and chicken consumption, y (in annual pounds per person), and found the consumption of beef declining and the consumption of chicken increasing
In Exercise 11.65, you used the analysis of variance procedure to analyze a 2 Ã— 3 factorial experiment in which each factor-level combination was replicated five times. The experiment involved the number of eggs laid by caged female whiteflies on two different plants at three different
The Academic Performance Index (API), described in Exercise 12.13, is a measure of school achievement based on the results of the Stanford 9 Achievement Test. The API scores for 12 elementary schools in Riverside County, California, are shown below, along with several other independent
Particle Board A quality control engineer is interested in predicting the strength of particle board y as a function of the size of the particles x1 and two types of bonding compounds. If the basic response is expected to be a quadratic function of particle size, write a linear model that
In a study to examine the relationship between the time required to complete a construction project and several pertinent independent variables, an analyst compiled a list of four variables that might be useful in predicting the time to completion. These four variables were size of the contract, x1
Groups of 10- day-old chicks were randomly assigned to seven treatment groups in which a basal diet was supplemented with 0, 50, 100, 150, 200, 250, or 300 micrograms/kilogram (g/kg) of biotin. The table gives the average biotin intake (x) in micrograms per day and the average weight gain (y) in
A department store conducted an experiment to investigate the effects of advertising expenditures on the weekly sales for its men's wear, children's wear, and women's wear departments. Five weeks for observation were randomly selected from each department, and an advertising budget x1 (in hundreds
Refer to Exercise 13.26. Use a computer software package to perform the multiple regression analysis and obtain diagnostic plots if possible.a. Comment on the fit of the model, using the analysis of variance F-test, R2, and the diagnostic plots to check the regression assumptions.b. Find the
A short-term study was conducted to investigate the effect of mean monthly daily temperature x1 and cost per kilowatt-hour x2 on the mean daily consumption of electricity (in kilowatt-hours, kWh) per household. The investigators expected the demand for electricity to rise in cold weather (due to
Because dolphins (and other large marine mammals) are considered to be the top predators in the marine food chain, the heavy metal concentrations in striped dolphins were measured as part of a marine pollution study. The concentration of mercury, the heavy metal reported in this study, is expected
Suppose that you fit the model E(y) = β0 + β1x1 + β2x2 + β3x3 to 15 data points and found F equal to 57.44. a. Do the data provide sufficient evidence to indicate that the model contributes information for the prediction of y? Test using a 5% level of significance. b. Use the value of F to
The quantitative reasoning scores on the Graduate Record Examination (GRE)7 were recorded for students admitted to three different graduate programs at a local university. This data was analyzed in Exercise 11.27 using the analysis of variance for a completely randomized design.a. Write the
Until recently, performance tires were fitted mostly on sporty or luxury vehicles. Now they come standard on many everyday sedans. Increased levels of handling and grip have come at the expense of tread wear. The data that follows is abstracted from a report on all-season tires by Consumer Reports8
The tuna fish data from Exercise 11.16 were analyzed as a completely randomized design with four treatments. However, we could also view the experimental design as a 2 Ã— 2 factorial experiment with unequal replications. The data are shown below.9The data can be analyzed using the
Refer to Exercise 13.32. The hypothesis tested in Chapter 11-that the average prices for the four types of tuna are the same-is equivalent to saying that E(y) will not change as x1 and x2 change. This can only happen when β1 = β2 = β3 = 0. Use the MINITAB printout for the one-way ANOVA shown
A manufacturer recorded the number of defective items (y) produced on a given day by each of 10 machine operators and also recorded the average output per hour (x1) for each operator and the time in weeks from the last machine service (x2).The printout that follows resulted when these data were
In an investigation to determine the relationship between the degree of metal corrosion and the length of time the metal is exposed to the action of soil acids, the percentage of corrosion and exposure time were measured weekly.The data were fitted using the quadratic model,E(y) = Î²0 + Î²1x +
A particular savings and loan corporation is interested in determining how well the amount of money in family savings accounts can be predicted using the three independent variables-annual income, number in the family unit, and area in which the family lives. Suppose that there are two specific
The computer output for the multiple regression analysis for Exercise 13.3 provides this information:a. Which, if any, of the independent variables x1, x2, and x3 contribute information for the prediction of y?b. Give the least-squares prediction equation.c. On the same sheet of graph paper, graph
Suppose that you fit the modelE(y) = Î²0 + Î²1x + Î²2x2to 20 data points and obtained the accompanying MINITAB printout.MINITAB output for Exercise 13.5Regression Analysis: y versus x, x-sqThe regression equation isy = 10.6 + 4.44 x - 0.648 x-sqa. What type of model
Refer to Exercise 13.5. a. What is the prediction equation? b. Graph the prediction equation over the interval 0 < x < 6.
Refer to Exercise 13.5. a. What is your estimate of the average value of y when x = 0? b. Do the data provide sufficient evidence to indicate that the average value of y differs from 0 when x = 0?
Refer to Exercise 13.5. a. Suppose that the relationship between E(y) and x is a straight line. What would you know about the value of b2? b. Do the data provide sufficient evidence to indicate curvature in the relationship between y and x?
Refer to Exercise 13.5. Suppose that y is the profit for some business and x is the amount of capital invested, and you know that the rate of increase in profit for a unit increase in capital invested can only decrease as x increases. You want to know whether the data provide sufficient evidence to
The case study in Chapter 12 examined the effect of foreign competition in the automotive industry as the number of imported cars steadily increased during the 1970s and 1980s.10 The U.S. automobile industry has been besieged with complaints about product quality, worker layoffs, and high prices
Medical statistics show that deaths due to four major diseases-call them A, B, C, and D-account for 15%, 21%, 18%, and 14%, respectively, of all non accidental deaths. A study of the causes of 308 non accidental deaths at a hospital gave the following counts:
Research has suggested a link between the prevalence of schizophrenia and birth during particular months of the year in which viral infections are prevalent. Suppose you are working on a similar problem and you suspect a linkage between a disease observed in later life and month of birth. You have
Suppose you are interested in following two independent traits in snap peas-seed texture (S = smooth, s = wrinkled) and seed color (Y = yellow, y = green)-in a second-generation cross of heterozygous parents. Mendelian theory states that the number of peas classified as smooth and yellow, wrinkled
The Mars, Incorporated website reported the following percentages of the various colors of its M&M'S candies for the "milk chocolate" variety:2A 14-ounce bag of milk chocolate M&M'S is randomly selected and contains 70 brown, 72 yellow, 61 red, 118 blue, 108 orange, and 85 green candies. Do the
The percentage of various colors are different for the "peanut" variety of M&M'S candies, as reported on the Mars, Incorporated website:3 A 14-ounce bag of peanut M&M'S is randomly selected and contains 70 brown, 87 yellow, 64 red, 115 blue, 106 orange, and 85 green candies. Do the data
Previous enrollment records at a large university indicate that of the total number of persons who apply for admission, 60% are admitted unconditionally, 5% are admitted on a trial basis, and the remainder are refused admission. Of 500 applications to date for the coming year, 329 applicants have
Calculate the value and give the number of degrees of freedom for X2 for these contingency tables:a.b.
Suppose that a consumer survey summarizes the responses of n = 307 people in a contingency table that contains three rows and five columns. How many degrees of freedom are associated with the chi-square test statistic?
A survey of 400 respondents produced these cell counts in a 2 Ã— 3 contingency table:a. If you wish to test the null hypothesis of "independence"- that the probability that a response falls in any one row is independent of the column it falls in-and you plan to use a chi-square test,
Male and female respondents to a questionnaire on gender differences were categorized into three groups according to their answers on the first question:Use the MINITAB printout to determine whether there is a difference in the responses according to gender. Explain the nature of the differences,
Congress passed the Health Care Reform Act in 2010 that will require all small businesses to have a health plan in place by 2014 and included the provision that no one could be denied coverage due to pre-existing conditions. A Newsweek Poll based on n 848 registered voters nationwide asked
A study was conducted by Joseph Jacobson and Diane Wille to determine the effect of early child care on infant-mother attachment patterns.5 In the study, 93 infants were classified as either "secure" or "anxious" using the Ainsworth strange situation paradigm. In addition, the infants were
Is there a difference in the spending patterns of high school seniors depending on their gender? A study to investigate this question focused on 196 employed high school seniors. Students were asked to classify the amount of their earnings that they spent on their car during a given month:A portion
The hair and eye color that follows was self-reported by a sample of Caucasian Americans born between 1957 and 1965 (currently 45-53 years old).6 The following data was adapted from that study.a. Is there sufficient evidence to conclude that the proportion of individuals with these hair colors
Almost50 years after the assassination of John F. Kennedy, a FOX News poll shows most Americans disagree with the government's conclusions about the killing. The Warren Commission found that Lee Harvey Oswald acted alone when he shot Kennedy, but many Americans are not so sure. Do you think that we
As an alternative to flextime, many companies allow employees to do some of their work at home. Individuals in a random sample of 300 workers were classified according to salary and number of workdays per week spent at home.a. Do the data present sufficient evidence to indicate that salary is
An article in American Demographics addressed the same telecommuting issue (Exercise 14.25) in a slightly different way. They concluded that "people who work exclusively at home tend to be older and better educated than those who have to leave home to report to work."8 Use the data below based on
Random samples of 200 observations were selected from each of three populations, and each observation was classified according to whether it fell into one of three mutually exclusive categories:You want to know whether the data provide sufficient evidence to indicate that the proportions of
Suppose you wish to test the null hypothesis that three binomial parameters pA, pB, and pC are equal versus the alternative hypothesis that at least two of the parameters differ. Independent random samples of 100 observations were selected from each of the populations. The data are shown in the
How do Americans in the "sandwich generation" balance the demands of caring for older and younger relatives? In a telephone poll of Americans aged 45-55 years conducted by the New York Times,9 the number providing financial support for their parents is listed in the next display.Is there a
Give the rejection region for a chi-square test of specified probabilities if the experiment involves k categories in these cases:a. k = 7, a = .05 b. k = 10, a = .01
A particular poultry disease is thought to be non communicable. To test this theory, 30,000 chickens were randomly partitioned into three groups of 10,000. One group had no contact with diseased chickens, one had moderate contact, and the third had heavy contact. After a 6-month period, data were
A study conducted in northwest England made an assessment of long-term care facilities that have residents with dementia.10 The homes included those that provided specialized services for elderly people with mental illness/health problems, known as "EMI homes," as well as others classified as
W.W. Menard has conducted research involving manganese nodules, a mineral-rich concoction found abundantly on the deep sea floor.11 In one portion of his report, Menard provides data relating the magnetic age of the earth's crust to the "probability of finding manganese nodules." The table gives
A local chamber of commerce surveyed 120 households in their city-40 in each of three types of residence (apartment, duplex, or single residence)-and recorded the number of family members in each of the households. The data are shown in the table.Is there a significant difference in the family size
According to a poll by the Pew Research Center, 55% of young adults (ages 18-29) believe that evolution is the best explanation for the development of human life.12 When the data are further categorized by whether or not the responders had a religious affiliation, this proportion changed for those
A manufacturer of floor polish conducted a consumer preference experiment to see whether a new floor polish A was superior to those produced by four competitors, B, C, D, and E. A sample of 100 housekeepers viewed five patches of flooring that had received the five polishes, and each indicated the
A survey was conducted to determine whether adult participation in physical fitness programs varies from one region of the United States to another. A random sample of people were interviewed in each of four states and these data were recorded:Do the data indicate a difference in adult
Accident data were analyzed to determine the numbers of fatal accidents for automobiles of three sizes. The data for 346 accidents are as follows:Do the data indicate that the frequency of fatal accidents is dependent on the size of automobiles? Write a short paragraph describing your statistical
An experiment was conducted to investigate the effect of general hospital experience on the attitudes of physicians toward Medicare patients. A random sample of 50 physicians who had just completed 4 weeks of service in a general hospital were categorized according to their concern for Medicare
Two biology instructors set out to evaluate the effects of discovery-based teaching compared to the standard lecture-based teaching approach in the laboratory.13 The standard lecture-based approach provided a list of instructions to follow at each step of the laboratory exercise, whereas the

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