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introduction to probability statistics
Introduction To Probability And Statistics 3rd Edition William Mendenhall - Solutions
14.44 Parking at the University A survey was conducted to determine student, faculty, and admin- istration attitudes about a new university parking policy. The distribution of those favouring or opposing the policy is shown in the table. Do the data provide sufficient evidence to indicate that
14.46 Fitting a Binomial Distribution You can use a goodness-of-fit test to determine whether all of the criteria for a binomial experiment have actually been met in a given application. Suppose that an experiment consisting of four trials was repeated 100 times. The number of repetitions on which
14.47 Antibiotics and Infection Infections some- times occur when blood transfusions are given during surgical operations. An experiment was conducted to determine whether the injection of antibodies reduced the probability of infection. An examination of the records of 138 patients produced the
14.48 German Manufacturing Canadian labour unions have traditionally been content to leave the management of the company to managers and corpo- rate executives. But in Europe, worker participation in management decision making is an accepted idea that is continually spreading. To study the effect
14.49 Three Entrances An occupant-traffic study was conducted to aid in the remodelling of an office building that contains three entrances. The choice of entrance was recorded for a sample of 200 persons who entered the building. Do the data in the table indicate that there is a difference in
14.50 Graduate Teaching Assistants Graduate students' responsibilities are often related to their roles as teaching assistants or research assistants. As part of a larger study, K.M. McGoldrick and her colleagues investigated the level of preparation of economics graduate students for their
14.51 Publish or Perish In the academic world, students and their faculty advisors often collaborate on research papers, producing works in which publica- tion credit can take several forms. In theory, the first authorship of a student's paper should be given to the student unless the input from
14.52 Are You a Good Driver? How would you rate yourself as a driver? According to a survey, most Albertans think they are good drivers but have little respect for others' driving ability. The data show the distribution of opinions according to gender for two different questions, the first rating
14.53 Vehicle Colours Each model year seems to introduce new colours and different hues for a wide array of vehicles, from luxury cars to full-size or intermediate models, to compacts and sports cars, to light trucks. However, white and silver/grey continue to make the top five or six colours
14.54 Vehicle Colours, again Refer to Exercise 14.53. The researcher wants to see if there is a difference in the colour distributions for compact/sports cars versus full/intermediate cars. 18 Another random sample of 250 full/intermediate cars was taken and the colour of the vehicles was recorded.
14.55 Good Tasting Medicine Pfizer Canada Inc. is a pharmaceutical company that makes azithromycin, an antibiotic in a cherry-flavoured suspension used to treat bacterial infections in children. To compare the taste of their product with three competing medications, Pfizer tested 50 healthy
14.56 Funny Cards When you choose a greeting card, do you always look for a humorous card, or does it depend on the occasion? A comparison sponsored by two of the nation's leading manufacturers of greeting cards indicated a slight difference in the proportions of humorous designs made for three
14.57 Rugby Injuries Knee injuries are a major problem for athletes in many contact sports. However, athletes who play certain positions are more prone to knee injuries than other players, and their injuries tend to be more severe. The preva- lence and patterns of knee injuries among women
14.58 Favourite Fast Foods The number of Canadians who visit fast-food restaurants regularly has grown steadily over the past decade. For this reason, marketing experts are interested in the demographics of fast-food customers. Is a customer's preference for a fast-food chain affected by the age of
14.59 Catching a Cold Is your chance of getting a cold influenced by the number of social contacts you have? A recent study showed that the more social relationships you have, the less susceptible you are to colds.22 A group of 276 healthy men and women were grouped according to their number of
14.60 Crime and Educational Achieve- ment A criminologist studying criminal offenders who have a record of one or more arrests is interested in knowing whether the educational achieve- ment level of the offender influences the frequency of arrests. He has classified his data using four educa-
14.61 More Business on the Weekends A department store manager claims that her store has twice as many customers on Fridays and Saturdays than on any other day of the week (the store is closed on Sundays). That is, the probability that a customer visits the store Friday is 2/8, the probability that
1. Perform a test of homogeneity for each question and verify the reported p-value of the test.Carole Day and Del Lowenthal studied the responses of young adults in their eval- uation of library services.23 Of the n = 200 young adults involved in the study, n = 152 were students and n = 48 were
2. Questions 3, 4, and 7 are concerned with the atmosphere of the library; questions 5 and 6 are concerned with the library staff; and questions 11 and 13 are concerned with the library design. How would you summarize the results of your analyses regarding these seven questions concerning the image
3. With the information given, is it possible to do any further testing concerning the proportion of favourable versus unfavourable responses for two or more questions simultaneously?Carole Day and Del Lowenthal studied the responses of young adults in their eval- uation of library services.23 Of
Canada has a Road Safety Vision of having the safest roads in the world. Yet the lead- ing cause of death of Canadian children remains vehicle crashes. In 2006, a national child safety seat survey was conducted by an AUTO21 research team in collaboration with Transport Canada to empirically measure
Social/behavioural scientists are usually interested in knowing what are the important issues for Canadian singles when it comes to dating. The print/digital media also has a keen interest in broadcasting these and other related issues. An example of this can be found in an online survey,
14.45 The chi-square test used in Exercise 14.43 is equivalent to the two-tailed z test of Section 9.6 provided a is the same for the two tests. Show algebra- ically that the chi-square test statistic x2 is the square of the test statistic z for the equivalent test.
14.17 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?
Refer to Example 14.3. Do the data present sufficient evidence to indicate that the type of furniture defect varies with the shift during which the piece of furniture is produced?
14.15 Admission Standards 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
14.12 Snap Peas Suppose you are interested in following two independent traits in snap peas-seed texture (S smooth, s wrinkled) and seed colour (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,
14.8 Peonies A peony plant with red petals was crossed with another plant having streaky petals. A geneticist states that 75% of the offspring from this cross will have red flowers. To test this claim, 100 seeds from this cross were collected and germinated, and 58 plants had red petals. Use the
14.4 Use Table 5 in Appendix I to bound the p-value for a chi-square test:a. x2 4.29, df 5b. x 20.62, df = 6c. x = 0.81, df = 5d. x 25.40, df = 13
14.3 Give the rejection region for a chi-square test of specified probabilities if the experiment involves k categories in these cases:a. k=7, = 0.05b. k 10, a 0.01c. k = 14, a 0.005d. k=3, a = 0.01
14.2 Use Table 5 in Appendix I to find the value of xwith the following area a to its right: -a. a 0.05, df = 3b. a = 0.01, df = 8d. = 0.01, df = 11c. = 0.005, df = 15
14.1 List the characteristics of a multinomial experiment.
How to Determine the Appropriate Number of Degrees of Freedom
Boreal mixedwood forests have been commercially logged for conifers, transected by roads and seismic cutlines, and regionally fragmented by agricultural practices. Most recently, Alberta's public mixedwood forests have been allocated for harvest of trembling aspen for pulp, paper, and oriented
4. What is the increase in R when you compare the fitted cubic with the fitted qua- dratic model? Is the fitted cubic model significantly better than the fitted quadratic? Are there any patterns in a plot of the residuals versus x? What proportion of the variation in the response Y is not accounted
3. What is the increase in R when you fit a quadratic rather than a linear model? Is the coefficient of the quadratic term significant? Is the fitted quadratic model signifi- cantly better than the fitted linear model? Plot the residuals from the fitted quadratic model. Does there seem to be any
2. Find the residuals using the fitted linear regression model. Does there appear to be any pattern in the residuals when plotted against x? What model do the residuals indicate would produce a better fit?The case study in Chapter 12 examined the effects of government regulation on for- eign
1. Plot the data and sketch what you consider to be the best-fitting linear, quadratic, and cubic models.The case study in Chapter 12 examined the effects of government regulation on for- eign ownership of assets in Canada. For example, the Foreign Investment Review Agency was created in 1975 to
13.37 Managing your Money 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
13.36 Metal Corrosion and Soil Acids 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
13.35 Quality Control 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
13.34 Tuna, continued Refer to Exercise 13.33. 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 x and x2 change. This can only happen when = = B3 0. Use the MINITAB printout for the one-way ANOVA
13.33 Tuna Fish 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 2 factorial experiment with unequal replications. The data are shown below.The data can be analyzed using the model
13.32 On the Road Again 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
13.31 Digital Video Recorders Digital video recorders (DVR) allow you to record and view programs at whatever time you request. Programs can be paused while you go to the kitchen for a snack, and commercials can be eliminated. The sales of DVRs have skyrocketed in the past couple of years, as shown
13.30 Cricket by Chance Is it true that the more balls a cricketer plays the more runs you make? The following table provides the related information about some of the cricket superstars from four countries for the year 2006. The data shown in this table give the total number of runs scored and
13.29 Mercury Concentration in Dolphins 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
13.28 Demand for Utilities Utility companies, which must plan the operation and expansion of electricity generation, are vitally inter- ested in predicting customer demand over both short and long periods of time. A short-term study was conducted to investigate the effect of mean monthly daily
13.26 Advertising and Sales 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
13.25 Biotin Intake in Chicks 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 (ug/kg) of biotin. The table gives the average biotin intake (x) in micrograms per day and the
13.24 Construction Projects 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
13.22 Blood Pressure Again! Refer to Exer- cise 12.29. The systolic blood pressure (SBP) for randomly selected 40 males and females are shown below, along with several other independent variables.The variables are defined as y = systolic blood pressure x = body mass index x2 = age X2 x3 = 1 if
13.21 Cotton versus Cucumber In Exercise 11.63, you used the analysis of variance proce- dure to analyze a 2 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
13.20 Less Red Meat! Canadians are very vocal about their attempts to improve personal well-being by "eating right and exercising more." One desirable dietary change is to reduce the intake of red meat and to substitute poultry or fish. Researchers tracked beef and chicken consumption, Y (in annual
Random samples of six female and six male assistant professors were selected from among the assistant professors in a university. The data on salary and years of experi- ence are shown in Table 13.3. Note that both samples contained two professors with 3 years of experience, but no male professor
13.16 Lexus, Inc. In Exercise 12.82, we presented sales data for the Lexus GX, a mid-size sport utility vehicle (SUV) sold in North American and Eurasian markets. The sales of the Lexus GX 470 from its inception until 2009 are given in the table:a. Plot the data. What model would you expect to
13.15 Corporate Profits In order to study the relationship of advertising and capital invest- ment 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
13.14 Air Pollution An experiment was designed to compare several different types of air pollution monitors. Each monitor was set up and then exposed to different concentrations of ozone, ranging between 15 and 230 parts per million (ppm), for periods of 8-72 hours. Filters on the monitor were then
13.13 Veggie-Burgers II 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 four independent variables. The printout is provided here.a. If you had to compare these models and choose the best one,
13.12 Veggie-Burgers You have a hot grill and an empty hamburger bun, but you have sworn off greasy hamburgers. Would a meatless hamburger do? The data in the table record a flavour and texture score (between 0 and 100) for 12 brands of meatless hamburgers along with the price, number of calories,
13.10 University Textbooks A publisher of university textbooks conducted a study to relate profit per text Y to cost of sales x over a six-year period when its sales force (and sales costs) were growing rapidly. These inflation-adjusted data (in thousands of dollars) were collected:Expecting profit
13.5 Suppose that you fit the model E(Y) = Bo + Box + B to 20 data points and obtained the accompanying MINITAB printout.b. How well does the model fit the data? Explain.c. Do the data provide sufficient evidence to indicate that the model contributes information for the pre- diction of y? Use the
In a study of variables that affect productivity in the retail grocery trade, W.S. Good uses value added per work-hour to measure the productivity of retail grocery outlets. He defines "value added" as "the surplus [money generated by the business] available to pay for labour, furniture and
How do real estate agents decide on the asking price for a newly listed condominium? A computer database in a small community contains the listed selling price Y (in thou- sands of dollars), the amount of living area x (in hundreds of square metres), and the numbers of floors x2, bedrooms x3, and
Boreal mixedwood forests have been commercially logged for conifers, transected by roads and seismic cutlines, and regionally fragmented by agricultural practices. Most recently, Alberta's public mixedwood forests have been allocated for harvest of trembling aspen for pulp, paper, and oriented
7. Given the form of the scatterplot, does it appear that a straight line provides an accurate model for the data? What other type of model might be more appropriate? (Use residual plots to help answer the question.)Canada's for sale! We're losing our sovereignty! Dire statements such as these
6. Add the data for 1986-2004 to your database, and recalculate the regression line. What effect have the new data points had on the slope? What is the effect on SSE?Canada's for sale! We're losing our sovereignty! Dire statements such as these frequently appear in the media when news breaks about
5. Now look at the actual data points for those years. Do the predictions obtained in step 4 provide accurate estimates of the actual values observed in these years? Explain.Canada's for sale! We're losing our sovereignty! Dire statements such as these frequently appear in the media when news
4. Use the computer program to predict the percentage of foreign ownership with 95% confidence intervals for the years 2002, 2003, and 2004.Canada's for sale! We're losing our sovereignty! Dire statements such as these frequently appear in the media when news breaks about a well-known Canadian
3. Is there a significant linear relationship between the percentage of foreign owner- ship and year?Canada's for sale! We're losing our sovereignty! Dire statements such as these frequently appear in the media when news breaks about a well-known Canadian company being pur- chased by a foreign
2. Use a computer software package to find the least-squares line for predicting the percentage of foreign ownership as a function of year for the years 1975-1985.Canada's for sale! We're losing our sovereignty! Dire statements such as these frequently appear in the media when news breaks about a
1. Using a scatterplot, plot the data for the years 1975-1985. Does there appear to be a linear relationship between the percentage of foreign ownership and the year?Canada's for sale! We're losing our sovereignty! Dire statements such as these frequently appear in the media when news breaks about
12.83 Starbucks Here is some nutritional Here data for a sampling of Starbucks 475 mL espresso beverages, made with 2% milk. The nutritional information for all of Starbucks products can be found on the company website, www. starbucks.com.Use the appropriate statistical methods to analyze the
12.82 Lexus, Inc. The Lexus GX is a mid- size sport utility vehicle (SUV) sold in North American and Eurasian markets. 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
12.81 Fresh Roses 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
12.80 Oatmeal, Anyone? An agricultural experimenter, investigating the effect of the amount of nitrogen x applied in 45 kg per hectare on the yield of oats y measured in 35 litres per hectare, collected the following data:a. Find the least-squares line for the data.b. Construct the ANOVA table.c.
12.79 If the experimenter stays within the experimental region, when will the error in predicting a particular value of y be maximum?
12.78 In addition to increasingly large bounds on error, why should an experimenter refrain from predicting y for values of x outside the experimental region?
12.76 Metabolism and Weight Gain Why is it that one person may tend to gain weight, even if he or she 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 identi- cal
12.75 Avocados II Refer to Exercise 12.74. Suppose the experimenter wants to examine the relationship between the penetrability and the number of days after harvest. Does the method of linear regres- sion discussed in this chapter provide an appropriate method of analysis? If not, what assumptions
12.74 Avocado Research 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
12.73 Tennis, Anyone? 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,
12.72 How Long Is It II? 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
12.71 Global Warming II? Refer to Exercise 12.13 and data set EX1213.a. Use an appropriate program to analyze the relationship between year and temperature anomaly.b. Explain all pertinent details of your analysis.
12.70 Knee Injuries Athletes and others suffering the same type of injury to the knee often require anterior and posterior ligament reconstruction. In order to determine the proper length of bone-patellar tendon-bone grafts, experiments were done using three imaging techniques to determine the
12.69 Nematodes Some varieties of nematodes, roundworms that live in the soil and frequently are so small as to be invisible to the naked eye, feed on the roots of lawn grasses and other plants. This pest, which is particularly troublesome in warm climates, can be treated by the application of
12.68 Track Stats! An experiment was conducted to investigate the effect of a training program on the length of time for a typical male uni- versity student to complete the 100-metre dash. Nine students were placed in the program. The reduction y in time to complete the 100-metre dash was measured
12.67 Plant Science An experiment was conducted to determine the effect of soil applications of various levels of phosphorus on the inor- ganic phosphorus levels in a particular plant. The data in the table represent the levels of inorganic phosphorus in micromoles (mol) per gram dry weight of
12.66 Potency of an Antibiotic An experiment was conducted to observe the effect of an increase in temperature on the potency of an antibiotic. Three 28-gram portions of the antibiotic were stored for equal lengths of time at each of these temperatures: -1.1C, 10C, 21.1C, and 32.2C. The potency
Refer to Table 12.1, in which the relationship between x = mathematics achievement test score and y = final calculus grade was studied.1. Enter the values for x and y into the first two columns of a MINITAB worksheet. 2. The main tools for linear regression analysis are generated using Stat
Refer to Table 12.1, in which the relationship between x = mathematics achievement test score and y = final calculus grade was studied.1. Enter the values for x and y into columns A and B of an Excel spreadsheet. 2. Use Data Data Analysis Regression to generate the dialogue box in Figure 12.18(a).
12.65 Baseball Stats 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.a. Plot the points using a
12.64 Cricket by Chance One measure of form for a bowler is the average run rate, defined as the number of runs given per wicket taken. A bowler is considered to be efficient if the run rate is close to optimum. The data shown in the following table provide information for 10 cricket bowlers from
12.63 Body Temperature and Heart Rate 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.a. Find the correlation
12.62 Cheese, Please! The demand for healthy foods that are low in fat and calories has resulted in a large number of "low-fat" or "fat-free" products. The table shows the number of calories and the amount of sodium (in milligrams) per slice for five different brands of fat-free cheese.a. Should
12.61 Geothermal Power Geothermal power is an important source of energy. Since the amount of energy contained in 0.45 kg of water is a function of its temperature, you might wonder whether water obtained from deeper wells contains more energy per 0.45 kg. The data in the table are reproduced from
12.60 Hockey II Refer to Exercise 12.59. Marino calculated the sample correlation coefficient r for the stride rate and the average acceleration rate for the 69 skaters to be 0.36. Do the data provide sufficient evidence to indicate a correlation between stride rate and average acceleration for the
12.59 Hockey G.W. Marino investigated the variables related to a hockey player's ability to make a fast start from a stopped position.13 In the experi- ment, each skater started from a stopped position and attempted to move as rapidly as possible over a 6-metre distance. The correlation coefficient
12.58 Social Skills Training 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 behaviour ratings. For one such test, the pre- and posttest scores for the seven students are
12.57 Lobster The table gives the numbers of Octolasmis tridens and O. lowei barnacles on each of 10 lobsters." 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
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