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mathematics
mathematical applications for the management

Questions and Answers of Mathematical Applications for the Management

Is the law requiring disclosure of payments sufficient to protect against financial support skewing study results? Do you have any other recommendations?
Should common standards exist for claiming authorship of a study? What should be included in those standards?
What is medical ghostwriting? Is the practice of medical ghostwriting unethical?
One article on the topic of statistical errors in medical research listed 47 potential sources of error. Try to identify 5 potential sources of error.
Reducing sample bias may result in a less positive outcome overall, which may delay or stop the release of a drug that a subset of the population might benefit from. Is this an acceptable tradeoff?
Volunteer bias is well documented on the topic of human sexuality. What are some other topics that might have high risk for volunteer bias?
Is it unethical to intentionally infect test subjects who are humans? What about animals?
For research projects that affect human subjects, is potential psychological harm any different from potential physical harm?
Was the Milgram experiment described in this section unethical? Why or why not?
Is it ethical to use prisoners as subjects if they understand the potential risks and have given their consent? Is it ethical to offer an incentive for consent, such as additional privileges or a
Conduct research to find a description of Deming’s funnel experiment, then use a funnel and marbles to collect data for the different rules for adjusting the funnel location. Construct appropriate
Exercises 5–8 in Section 14-1 used process data from the manufacture of 0.0109-in.-thick aluminum cans. Refer to Data Set 30 “Aluminum Cans” in Appendix B and conduct an analysis of the process
a. Simulate the following process for 20 days: Each day, 200 calculators are manufactured with a 5% rate of defects, and the proportion of defects is recorded for each of the 20 days. The calculators
Based on the survey data given in Exercise 1, assume that 55% of adults learn about medical symptoms more often from the Internet than from their doctor.a. Find the probability that three randomly
The SmartBatt company manufactures batteries for smartphones. Listed below are numbers of defects in batches of 200 batteries randomly selected in each of 12 consecutive days of production. What
In each of several consecutive days of production of cola cans, 50 cans are tested and the numbers of defects each day are listed below. Do the proportions of defects appear to be acceptable? What
Consider a process of minting coins with a value of one euro. Listed below are the numbers of defective coins in successive batches of 10,000 coins randomly selected on consecutive days of
After constructing a control chart for the proportions of defective one-euro coins, it is concluded that the process is within statistical control. Does it follow that almost all of the coins meet
In constructing a control chart for the proportions of defective dimes, it is found that the lower control limit is -0.00325. How should that value be adjusted?
An x̅̅ chart based on standard deviations (instead of ranges) is constructed by plotting sample means with a centerline at x̅̅ and control limits at x̅̅ + A3x̅ and x̅̅ - A3x̅, where A3 is
An x̅̅ chart based on standard deviations (instead of ranges) is constructed by plotting sample means with a centerline at x̅̅ and control limits at x̅̅ + A3x̅ and x̅̅ - A3x̅, where A3 is
Find the values of x̅̅ and R̅̅. Also find the values of LCL and UCL for an R chart, then find the values of LCL and UCL for an x̅̅ chart.Refer to the accompanying table of weights (grams) of
Consider process data consisting of the amounts (oz) of Coke in randomly selected cans of regular Coke. The process is to be monitored with x and R control charts based on samples of 50 cans randomly
Table 14-1 on page 655 lists process data consisting of the errors (ft) of aircraft altimeters when they are tested for an altitude of 2000 ft, and the Federal Aviation Administration requires that
Divide into groups of three or four students. Investigate the relationship between two variables by collecting your own paired sample data and using the methods of Section 13-6 to determine whether
Divide into groups of three or four students. Investigate the relationship between two variables by collecting your own paired sample data and using the methods of Section 13-6 to determine whether
Past attempts to identify or contact extraterrestrial intelligent life have involved efforts to send radio messages carrying information about us earthlings. Dr. Frank Drake of Cornell University
Advances in technology are dramatically affecting different aspects of our lives. For example, the number of daily print newspapers is decreasing because of easy access to Internet and television
Refer to the following ages at inauguration of the elected presidents of the United States (from Data Set 15 “Presidents” in Appendix B). Test for randomness above and below the mean. Do the
Each year, U.S. News & World Report publishes rankings of colleges based on statistics such as admission rates, graduation rates, class size, faculty–student ratio, faculty salaries, and peer
Listed below are the costs (in dollars) of eight different flights from New York (JFK) to San Francisco for Virgin America, US Airways, United Airlines, JetBlue, Delta, American Airlines, Alaska
Listed below are time intervals (min) between eruptions of the Old Faithful geyser. The “recent” times are within the past few years, and the “past” times are from 1995. Test the claim that
Listed below are the annual high values of the Dow Jones Industrial Average for a recent sequence of years. Find the median, then test for randomness below and above the median. What does the result
Test the claim that the sequence of World Series wins by American League and National League teams is random. Given on the next page are recent results, with A = American League and N = National
Listed below are the conference designations of teams that won the Super Bowl, where N denotes a team from the NFC and A denotes a team from the AFC. Do the results suggest that either conference is
Media experts claim that daily print newspapers are declining because of Internet access. Listed below are the numbers of daily print newspapers in the United States for a recent sequence of years.
In 1970, a lottery was used to determine who would be drafted into the U.S. Army. The 366 dates in the year were placed in individual capsules, they were mixed, and then capsules were selected to
A New York Times article about the calculation of decimal places of p noted that “mathematicians are pretty sure that the digits of π are indistinguishable from any random sequence.” Given below
An alternative to using Table A–9 to find critical values for rank correlation is to compute them using this approximation:Here, t is the critical t value from Table A-3 corresponding to the
Refer to the measured systolic and diastolic blood pressure measurements of 153 randomly selected males in Data Set 1 “Body Data” in Appendix B and use 0.05 significance level to test the claim
Listed below are ages of Best Actresses and Best Actors at the times they won Oscars (from Data Set 14 “Oscar Winner Age” in Appendix B). Do these data suggest that there is a correlation between
Use the scatterplot to find the value of the rank correlation coefficient rs and the critical values corresponding to a 0.05 significance level used to test the null hypothesis of ρs = 0. Determine
Refer to Table 13-2 on page 600 and identify the efficiency of the rank correlation test. What does that value tell us about the test?Table 13-2:
If the methods of this section are used with paired sample data, and the conclusion is that there is sufficient evidence to support the claim of a correlation between the two variables, can we use
In using the Kruskal-Wallis test, there is a correction factor that should be applied whenever there are many ties: Divide H byFirst combine all of the sample data into one list, and then, in that
Listed below are highway fuel consumption amounts (mi/gal) for cars categorized by the sizes of small, midsize, and large (from Data Set 20 “Car Measurements” in Appendix B). Using a 0.05
Use the following listed chest deceleration measurements (in g, where g is the force of gravity) from samples of small, midsize, and large cars. (These values are from Data Set 19 “Car Crash
Use the following listed chest deceleration measurements (in g, where g is the force of gravity) from samples of small, midsize, and large cars. (These values are from Data Set 19 “Car Crash
Use the sample data from Exercise 1 to test the claim that females from the different age brackets give attribute ratings with the same median. Use a 0.05 significance level.Use the Kruskal-Wallis
Refer to Table 13-2 on page 600 and identify the efficiency of the Kruskal-Wallis test. What does that value tell us about the test?Table 13-2:
Refer to Table 13-2 on page 600 and identify the efficiency of the Kruskal-Wallis test. What does that value tell us about the test?Table 13-2:
For the data given in Exercise 1, identify the values of n1, n2, n3, and N.Data From Exercise 1:Listed on the top of the next page are attribute ratings of males by females who participated in speed
Assume that we want to use the data from Exercise 1 with the Kruskal- Wallis test. Are the requirements satisfied? Explain.Data From Exercise 1:Listed on the top of the next page are attribute
The Mann-Whitney U test is equivalent to the Wilcoxon rank-sum test for independent samples in the sense that they both apply to the same situations and always lead to the same conclusions. In the
Data Set 7 “IQ and Lead” in Appendix B lists performance IQ scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects with high lead levels
Refer to Data Set 24 “Word Counts” in Appendix B and use the measured word counts from men in the third column and the measured word counts from women in the fourth column. Use a 0.01
In a study of students blanking out on tests, the arrangement of test items was studied for its effect on anxiety. The following scores are measures of “debilitating test anxiety” (based on data
In a study of students blanking out on tests, the arrangement of test items was studied for its effect on anxiety. The following scores are measures of “debilitating test anxiety” (based on data
Use the sample data given in Exercise 1 and test the claim that evaluation ratings of female professors have the same median as evaluation ratings of male professors. Use a 0.05 significance
Exercise 16 “Old Faithful”Refer to the sample data from the given exercises in Section 13-2 on page 611. Use the Wilcoxon signed-ranks test for the claim about the median of a population.Data
Exercise 15 “Testing for Median Weight of Quarters”Refer to the sample data from the given exercises in Section 13-2 on page 611. Use the Wilcoxon signed-ranks test for the claim about the median
Exercise 14 “Earthquake Depths”Refer to the sample data from the given exercises in Section 13-2 on page 611. Use the Wilcoxon signed-ranks test for the claim about the median of a
Exercise 13 “Earthquake MagnitudesRefer to the sample data from the given exercises in Section 13-2 on page 611. Use the Wilcoxon signed-ranks test for the claim about the median of a
Exercise 13 “Earthquake MagnitudesRefer to the sample data from the given exercises in Section 13-2 on page 611. Use the Wilcoxon signed-ranks test for the claim about the median of a
Exercise 7 “Speed Dating: Attributes”Refer to the sample data for the given exercises in Section 13-2 on page 611. Use the Wilcoxon signed-ranks test to test the claim that the matched pairs have
Exercise 5 “Speed Dating: Attributes”Refer to the sample data for the given exercises in Section 13-2 on page 611. Use the Wilcoxon signed-ranks test to test the claim that the matched pairs have
Exercise 8 “Speed Dating: Attractiveness”Refer to the sample data for the given exercises in Section 13-2 on page 611. Use the Wilcoxon signed-ranks test to test the claim that the matched pairs
Exercise 6 “Speed Dating: Attractiveness”Refer to the sample data for the given exercises in Section 13-2 on page 611. Use the Wilcoxon signed-ranks test to test the claim that the matched pairs
Exercise 5 “Speed Dating: Attributes”Refer to the sample data for the given exercises in Section 13-2 on page 611. Use the Wilcoxon signed-ranks test to test the claim that the matched pairs have
Refer to Table 13-2 on page 600 and identify the efficiency of the Wilcoxon signed-ranks test. What does that value tell us about the test?Table 13-2:
Table A-7 lists critical values for limited choices of a. Use Table A-1 to add a new column in Table A-7 (from n = 1 to n = 8) that represents a significance level of 0.03 in one tail or 0.06 in two
In the sign test procedure described in this section, we exclude ties (represented by 0 instead of a sign of + or -). A second approach is to treat half of the 0s as positive signs and half as
In the sign test procedure described in this section, we exclude ties (represented by 0 instead of a sign of + or -). A second approach is to treat half of the 0s as positive signs and half as
Refer to Data Set 29 “Coin Weights” in Appendix B for the weights (g) of randomly selected quarters that were minted after 1964. The quarters are supposed to have a median weight of 5.670 g. Use
Refer to Data Set 21 “Earthquakes” in Appendix B for the earthquake magnitudes. Use a 0.01 significance level to test the claim that the median is equal to 2.00.Refer to the indicated data set in
Refer to Data Set 21 “Earthquakes” in Appendix B for the earthquake magnitudes. Use a 0.01 significance level to test the claim that the median is equal to 2.00.Refer to the indicated data set in
In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were dropped or dismissed (based on data from the Physicians Insurers Association of America). Use a
Refer to Table 13-2 on page 600 and identify the efficiency of the sign test. What does that value tell us about the sign test?Table 13-2:
Divide into groups of three or four students. Each group should survey other students at the same college by asking them to identify their major and gender. You might include other factors, such as
Refer to Data Set 1 “Body Data” in Appendix B and use the weights of males partitioned into the three different age brackets of 18–25, 26–40, and 41–80. Test the claim that men in those
USA Today reported on an Adecco Staffng survey of 1000 randomly selected adults. Among those respondents, 20% chose health benefits as being most important to their job.a. What is the number of
Pages were randomly selected by the author from The Bear and the Dragon by Tom Clancy, Harry Potter and the Sorcerer’s Stone by J. K. Rowling, and War and Peace by Leo Tolstoy. The Flesch Reading
Example 1 illustrated the use of two-way ANOVA to analyze the sample data in Table 12-3. How are the results affected in each of the following cases?a. The same constant is added to each sample
The table below lists body temperatures obtained from randomly selected subjects (based on Data Set 3 “Body Temperatures” in Appendix B). Using a 0.05 significance level, test for an interaction
Listed below are ratings of pancakes made by experts (based on data from Minitab). Different pancakes were made with and without a supplement and with different amounts of whey. The results from
If we have a goal of using the data described in Exercise 1 to (1) determine whether age bracket has an effect on pulse rates and (2) to determine whether gender has an effect on pulse rates, should
Shown below are weights (kg) of poplar trees obtained from trees planted in a rich and moist region. The trees were given different treatments identified in the table below. The data are from a study
Shown below are weights (kg) of poplar trees obtained from trees planted in a rich and moist region. The trees were given different treatments identified in the table below. The data are from a study
A display of the Bonferroni test results from Table 12-1 (which is part of the Chapter Problem) is provided on page 577. Shown on the top of the next page is the SPSS-generated display of results
Refer to Data Set 12 “Passive and Active Smoke” in Appendix B and use the measured serum cotinine levels (in mg>mL) from the three groups of subjects (smokers, nonsmokers exposed to tobacco
Jeff Parent is a statistics instructor who participates in triathlons. Listed below are times (in minutes and seconds) he recorded while riding a bicycle for five stages through each mile of a 3-mile
Jeff Parent is a statistics instructor who participates in triathlons. Listed below are times (in minutes and seconds) he recorded while riding a bicycle for five stages through each mile of a 3-mile
If we use a 0.05 significance level in analysis of variance with the sample data given in Exercise 1, what is the P-value? What should we conclude? If a passenger abhors late flight arrivals, can
Refer to the sample data given in Exercise 1. If we want to test for equality of the three means, why don’t we use three separate hypothesis tests for μ1 = μ2, μ1 = μ3, and μ2 = μ3?Use the
a. What characteristic of the data above indicates that we should use one-way analysis of variance?b. If the objective is to test the claim that the three flights have the same mean arrival delay
Divide into groups of two or three students. The analysis of last digits of data can sometimes reveal whether values are the results of actual measurements or whether they are reported estimates.
Divide into groups of three or four students. Each group should be given a die along with the instruction that it should be tested for “fairness.” Is the die fair or is it biased? Describe the
Divide into groups of four or five students. Each group member should select about 15 other students and first ask them to “randomly” select four digits each. After the four digits have been
Divide into groups of four or five students. Each group member should survey at least 15 male students and 15 female students at the same college by asking two questions: (1) Which political party
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

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