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mathematics
mathematical applications for the management

Questions and Answers of Mathematical Applications for the Management

Divide into groups of four or five students and collect past results from a state lottery. Such results are often available on websites for individual state lotteries. Use the methods of Section 11-1
Divide into groups of four or five students. The Chapter Problem noted that according to Benford’s law, a variety of different data sets include numbers with leading (first) digits that follow the
Use Statdisk, Minitab, Excel, StatCrunch, a TI-83>84 Plus calculator, or any other software package or calculator capable of generating equally likely random digits between 0 and 9 inclusive.
When designing cars and aircraft, we must consider the forward grip reach of women. Women have normally distributed forward grip reaches with a mean of 686 mm and a standard deviation of 34 mm (based
Listed below are repair costs (in dollars) for cars crashed at 6 mi/h in full-front crash tests and the same cars crashed at 6 mi/h in full-rear crash tests (based on data from the Insurance
In a study of the “denomination effect,” 150 women in China were given either a single 100 yuan bill or a total of 100 yuan in smaller bills. The value of 100 yuan is about $15. The women were
Lipitor is the trade name of the drug atorvastatin, which is used to reduce cholesterol in patients. (Until its patent expired in 2011, this was the largest-selling drug in the world, with annual
Contestants on the TV show American Idol competed to win a singing contest. At one point, the website WhatNotToSing.com listed the actual numbers of eliminations for different orders of singing, and
The chi-square distribution is continuous, whereas the test statistic used in this section is discrete. Some statisticians use Yates’s correction for continuity in cells with an expected frequency
A x2 test involving a 2 × 2 table is equivalent to the test for the difference between two proportions, as described in Section 9-1. Using the claim and table in Exercise 9 “Four Quarters the Same
Winning team data were collected for teams in different sports, with the results given in the table on the top of the next page (based on data from “Predicting Professional Sports Game Outcomes
In his book Outliers, author Malcolm Gladwell argues that more American-born baseball players have birth dates in the months immediately following July 31 because that was the age cutoff date for
A study of people who refused to answer survey questions provided the randomly selected sample data shown in the table below (based on data from “I Hear You Knocking But You Can’t Come In,” by
A case-control (or retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results
In a clinical trial of the effectiveness of echinacea for preventing colds, the results in the table below were obtained (based on data from “An Evaluation of Echinacea Angustifolia in Experimental
A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the given table (based on data from “What Kinds of People Do Not Use Seat Belts?” by Helsing and
In soccer, serious fouls in the penalty box result in a penalty kick with one kicker and one defending goalkeeper. The table below summarizes results from 286 kicks during games among top teams
The table below shows results since 2006 of challenged referee calls in the U.S. Open. Use a 0.05 significance level to test the claim that the gender of the tennis player is independent of whether
A randomized controlled trial was designed to compare the effectiveness of splinting versus surgery in the treatment of carpal tunnel syndrome. Results are given in the table below (based on data
The accompanying TI-83/84 Plus calculator display results from the hypothesis test described in Exercise 1. Assume that the hypothesis test requirements are all satisfied. Identify the test statistic
Refer to Data Set 1 “Body Data” in Appendix B for the heights of females.a. Enter the observed frequencies in the table above.b. Assuming a normal distribution with mean and standard deviation
The author recorded the leading digits of the sizes of the electronic document files for the current edition of this book. The leading digits have frequencies of 55, 25, 17, 24, 18, 12, 12, 3, and 4
Frequencies of leading digits from IRS tax files are 152, 89, 63, 48, 39, 40, 28, 25, and 27 (corresponding to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively, based on data from
Exercise 21 lists the observed frequencies of leading digits from amounts on checks from seven suspect companies. Here are the observed frequencies of the leading digits from the amounts on the most
Exercise 21 lists the observed frequencies of leading digits from amounts on checks from seven suspect companies. Here are the observed frequencies of the leading digits from the amounts on the most
When working for the Brooklyn district attorney, investigator Robert Burton analyzed the leading digits of the amounts from 784 checks issued by seven suspect companies. The frequencies were found to
The table below lists the numbers of games played in 105 Major League Baseball (MLB) World Series. This table also includes the expected proportions for the numbers of games in a World Series,
The table below lists the frequency of wins for different post positions through the 141st running of the Kentucky Derby horse race. A post position of 1 is closest to the inside rail, so the horse
Repeat Exercise 11 using these observed frequencies for police calls received during the month of March: Monday (208); Tuesday (224); Wednesday (246); Thursday (173); Friday (210); Saturday (236);
The police department in Madison, Connecticut, released the following numbers of calls for the different days of the week during a February that had 28 days: Monday (114); Tuesday (152); Wednesday
In analyzing hits by V-1 buzz bombs in World War II, South London was subdivided into regions, each with an area of 0.25 km2. Shown below is a table of actual frequencies of hits and the frequencies
The author drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 27,
The accompanying Statdisk results shown in the margin are obtained from the data given in Exercise 1. What should be concluded when testing the claim that the leading digits have a distribution that
Divide into groups of three or four people. Investigate the relationship between two variables by collecting your own paired sample data and using the methods of this chapter to determine whether
Divide into groups of three or four people. Appendix B includes many data sets not yet included in examples or exercises in this chapter. Search Appendix B for a pair of variables of interest, then
Divide into groups of 8 to 12 people. Record the pulse rate of each group member while he or she is seated. Then record the pulse rate of each group member while he or she is standing. Is there a
Use a ruler as a device for measuring reaction time. One person should suspend the ruler by holding it at the top while the subject holds his or her thumb and forefinger at the bottom edge, ready to
Divide into groups of 8 to 12 people. For each group member, measure the person’s height and also measure his or her navel height, which is the height from the floor to the navel. Is there a
Divide into groups of 8 to 12 people. For each group member, measure the person’s height and also measure his or her navel height, which is the height from the floor to the navel. Is there a
Data Set 18 “Speed Dating” in Appendix B includes data from 199 dates. Due to the large size of this data set, the data are available at www.TriolaStats.com. Download the data set and proceed to
Based on the data from Cumulative Review Exercise 7, assume that ages of moviegoers are normally distributed with a mean of 35 years and a standard deviation of 20 years.a. What is the percentage of
Construct a 95% confidence interval estimate of the mean sunspot number. Write a brief statement interpreting the confidence interval.Listed below are annual high values of the Dow Jones Industrial
Use the sample data given in Review Exercise 1 “Cigarette Tar and Nicotine.”a. Find the multiple regression equation with the response (y) variable of amount of nicotine and predictor (x)
Refer to the table of data given in Exercise 1 and use the amounts of nicotine and carbon monoxide (CO).a. Construct a scatterplot using nicotine for the x scale, or horizontal axis. What does the
In addition to the value of R2, another measurement used to assess the quality of a model is the sum of squares of the residuals. Recall from Section 10-2 that a residual is the difference between an
In 1965, Intel cofounder Gordon Moore initiated what has since become known as Moore’s law: The number of transistors per square inch on integrated circuits will double approximately every 18
Listed below are mean annual temperatures (°C) of the earth for each decade, beginning with the 1880s. Find the best model and then predict the value for 2090– 2099. Comment on the
Listed below in order by row are annual sunspot numbers beginning with 1980. Is the best model a good model? Carefully examine the scatterplot and identify the pattern of the points. Which of the
Listed on the top of the next page in order by row are the annual high values of the Dow Jones Industrial Average for each year beginning with 1990. Find the best model and then predict the value for
The table lists different amounts (metric tons) of the explosive TNT and the corresponding value measured on the Richter scale resulting from explosions of the TNT.Construct a scatterplot and
The table lists the value y (in dollars) of $1000 deposited in a certificate of deposit at Bank of New York (based on rates currently in effect).Construct a scatterplot and identify the mathematical
The table lists the value y (in dollars) of $1000 deposited in a certificate of deposit at Bank of New York (based on rates currently in effect).Construct a scatterplot and identify the mathematical
The accompanying graph plots the numbers of points scored in each Super Bowl to the last Super Bowl at the time of this writing. The graph of the quadratic equation that best fits the data is also
In Exercise 2, the quadratic model results in R2 = 0.255. Identify the percentage of the variation in Super Bowl points that can be explained by the quadratic model relating the variable of year and
Refer to Data Set 9 “Bear Measurements” in Appendix B and use the sex,age, and weight of the bears. For sex, let 0 represent female and let 1 represent male. Letting the response (y) variable
Refer to Data Set 9 “Bear Measurements” in Appendix B and use the sex,age, and weight of the bears. For sex, let 0 represent female and let 1 represent male. Letting the response (y) variable
A confidence interval for the regression coefficient β1 is expressed aswhereThe critical t score is found using n - (k + 1) degrees of freedom, where k, n, and sb1 are described in Exercise 17.
If the coefficient β1 has a nonzero value, then it is helpful in predicting the value of the response variable. If β1 = 0, it is not helpful in predicting the value of the response variable and can
Refer to Data Set 7 “IQ and Lead” in Appendix B and find the best regression equation with IQ FULL (full IQ score) as the response (y) variable. Use predictor variables of IQ VERB (verbal IQ
Repeat the preceding exercise using the sample data from the Menthol cigarettes listed in Data Set 13 “Cigarette Contents” in Appendix B.Refer to the indicated data set in Appendix B and use
Refer to Data Set 13 “Cigarette Contents” in Appendix B and use the tar, nicotine, and CO amounts for the cigarettes that are 100 mm long, filtered, nonmenthol, and nonlight (the last set of
A Honda Civic weighs 2740 lb, it has an engine displacement of 1.8 L, and its highway fuel consumption is 36 mi/gal. What is the best predicted value of the city fuel consumption? Is that predicted
Which regression equation is best for predicting city fuel consumption? Why?Refer to the accompanying table, which was obtained using the data from 21 cars listed in Data Set 20 “Car
If exactly two predictor (x) variables are to be used to predict the city fuel consumption, which two variables should be chosen? Why?Refer to the accompanying table, which was obtained using the
If only one predictor (x) variable is used to predict the city fuel consumption, which single variable is best? Why?Refer to the accompanying table, which was obtained using the data from 21 cars
Should the multiple regression equation be used for predicting the height of a son based on the height of his father and mother? Why or why not?We want to consider the correlation between heights of
Identify the multiple regression equation that expresses the height of a son in terms of the height of his father and mother.We want to consider the correlation between heights of fathers and mothers
Example 1 in this section illustrated the procedure for finding a prediction interval for an individual value of y. When using a specific value x0 for predicting the mean of all values of y, the
The table below lists overhead widths (cm) of seals measured from photographs and the weights (kg) of the seals (based on “Mass Estimation of Weddell Seals Using Techniques of Photogrammetry,” by
Using x = 85 (for 850,000 registered boats), what is the single value that is the best predicted number of manatee fatalities resulting from encounters with boats?Refer to the display obtained by
What percentage of the total variation in manatee fatalities can be explained by the linear correlation between registered boats and manatee fatalities?Refer to the display obtained by using the
Use the information provided in the display to determine the value of the linear correlation coefficient. Is there sufficient evidence to support a claim of a linear correlation between numbers of
Using the heights and weights described in Exercise 1, a height of 180 cm is used to find that the predicted weight is 91.3 kg, and the 95% prediction interval is (59.0 kg, 123.6 kg). Write a
Using Data Set 1 “Body Data” in Appendix B, if we let the predictor variable x represent heights of males and let the response variable y represent weights of males, the sample of 153 heights and
According to the least-squares property, the regression line minimizes the sum of the squares of the residuals. Refer to the data in Table 10-1.a. Find the sum of squares of the residuals.b. Show
According to the least-squares property, the regression line minimizes the sum of the squares of the residuals. Refer to the data in Table 10-1.a. Find the sum of squares of the residuals.b. Show
Refer to Data Set 21 “Earthquakes” in Appendix B and use the depths (x) and magnitudes (y) from the earthquakes. Find the best predicted magnitude of an earthquake with a depth of 5 km.In each
Refer to Data Set 21 “Earthquakes” in Appendix B and use the depths (x) and magnitudes (y) from the earthquakes. Find the best predicted magnitude of an earthquake with a depth of 5 km.In each
Refer to Data Set 24 “Word Counts” in Appendix B and use the word counts measured from men (x) and women (y) in couple relationships listed in the first two columns of Data Set 24. Find the best
Repeat Exercise 18 using the foot lengths and heights of the 19 males from Data Set 2 “Foot and Height.”In each case, find the regression equation, letting the first variable be the predictor (x)
Repeat Exercise 17 using the shoe print lengths and heights of the 19 males from Data Set 2 “Foot and Height.”Exercise 17:Use the shoe print lengths and heights to find the best predicted height
Using the diameter/volume data from the preceding exercise, find the best predicted volume of a marble with a diameter of 1.50 cm. How does the result compare to the actual volume of 1.8 cm3?In each
Using the diameter/volume data from the preceding exercise, find the best predicted volume of a marble with a diameter of 1.50 cm. How does the result compare to the actual volume of 1.8 cm3?In each
Using the diameter/volume data from the preceding exercise, find the best predicted volume of a marble with a diameter of 1.50 cm. How does the result compare to the actual volume of 1.8 cm3?In each
Using the diameter/circumference data, find the best predicted circumference of a marble with a diameter of 1.50 cm. How does the result compare to the actual circumference of 4.7 cm?
Using the diameter/circumference data, find the best predicted circumference of a marble with a diameter of 1.50 cm. How does the result compare to the actual circumference of 4.7 cm?
Using the listed width/weight data, find the best predicted weight of a seal if the overhead width measured from a photograph is 2 cm. Can the prediction be correct? If not, what is wrong?
Refer to the Minitab-generated scatterplot given in Exercise 12 of Section 10-1 on page 485.a. Using the pairs of values for all 8 points, find the equation of the regression line.b. Using only the
Refer to the Minitab-generated scatterplot given in Exercise 12 of Section 10-1 on page 485.a. Using the pairs of values for all 8 points, find the equation of the regression line.b. Using only the
Refer to the Minitab-generated scatterplot given in Exercise 12 of Section 10-1 on page 485.a. Using the pairs of values for all 8 points, find the equation of the regression line.b. Using only the
Refer to the Minitab-generated scatterplot given in Exercise 12 of Section 10-1 on page 485.a. Using the pairs of values for all 8 points, find the equation of the regression line.b. Using only the
Refer to the Minitab-generated scatterplot given in Exercise 12 of Section 10-1 on page 485.a. Using the pairs of values for all 8 points, find the equation of the regression line.b. Using only the
Refer to the Minitab-generated scatterplot given in Exercise 11 of Section 10-1 on page 485.a. Using the pairs of values for all 10 points, find the equation of the regression line.b. After removing
For 30 recent Academy Award ceremonies, ages of Best Supporting Actors (x) and ages of Best Supporting Actresses (y) are recorded. The 30 paired ages yield x̅ = 52.1 years, y̅ = 37.3 years, r =
For 30 recent Academy Award ceremonies, ages of Best Supporting Actors (x) and ages of Best Supporting Actresses (y) are recorded. The 30 paired ages yield x̅ = 52.1 years, y̅ = 37.3 years, r =
Table A-6 lists critical values of r for selected values of n and a. More generally, critical r values can be found by using the formula where the t value is found from the table of critical t
In addition to testing for a linear correlation between x and y, we can often use transformations of data to explore other relationships. For example, we might replace each x value by x2 and use the
In addition to testing for a linear correlation between x and y, we can often use transformations of data to explore other relationships. For example, we might replace each x value by x2 and use the
Listed below are the overhead widths (cm) of seals measured from photographs and the weights (kg) of the seals (based on “Mass Estimation of Weddell Seals Using Techniques of Photogrammetry,” by
A classic application of correlation involves the association between the temperature and the number of times a cricket chirps in a minute. Listed below are the numbers of chirps in 1 min and the

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