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elementary statistics

Elementary Statistics 9th Edition Mario F. Triola - Solutions

Large Sample: Testing for Randomness of Marathon Runners Refer to Data Set 8 in Appendix B for the random sample of runners who finished the New York City marathon. The runners are listed in the order in which they finished. Test the sequence of genders for randomness. Is there sufficient evidence
Large Sample: Testing for Randomness of Odd and Even Digits in Pi A New York Times article about the calculation of decimal places of p noted that “mathematicians are pretty sure that the digits of p are indistinguishable from any random sequence.”
Testing for Randomness of Motor Vehicle Deaths Refer to Data Set 25 in Appendix B for the numbers of motor vehicle deaths in the United States for the preceding two decades. Test for randomness above and below the mean. Do the numbers of motor vehicle deaths appear to be random? If not, is there a
Stock Market: Testing for Randomness Above and Below the Median Trends in business and economics applications are often analyzed with the runs test. Data Set 25 in Appendix B lists the annual high points of the Dow-Jones Industrial Average for a recent sequence of years. First find the median of
Testing for Randomness of Selected Military Draft Dates Men were once drafted into the U.S. Army by using a process that was supposed to randomly select birthdays.Suppose the first few selections are as listed below. Test the sequence for randomness before and after the middle of the year.Nov. 27
Testing for Randomness of Presidential Election Winners For a recent sequence of presidential elections, the political party of the winner is indicated by D for Democrat and R for Republican. Does it appear that we elect Democrat and Republican candidates in a sequence that is
Testing for Randomness of Baseball World Series Victories Test the claim that the sequence of World Series wins by American League and National League teams is random. Given below are recent results with American and National league teams represented by A and N, respectively. What does the result
Testing for Randomness in Dating Prospects Fred has had difficulty getting dates with women, so he is abandoning his strategy of careful selection and replacing it with a desperate strategy of random selection. In pursuing dates with randomly selected women, Fred finds that some of them are
Testing for Randomness of Survey Respondents When selecting subjects to be surveyed about Infograme’s Roller Coaster Tycoon game, the subjects were selected in a sequence with the genders listed below. Does it appear that the subjects were randomly selected according to
Randomness of Roulette Wheel Outcomes In conducting research for this book, the author recorded the outcomes of a roulette wheel in the Stardust Casino. (Yes, it was hard work, but somebody had to do it.) Test for randomness of odd (O) and even (E)numbers for the results given in the following
Effect of Ties on rs Refer to Data Set 7 in Appendix B for the times (in seconds) of tobacco use and alcohol use depicted in animated children’s movies. Calculate the value of the test statistic rs by using each of the two formulas given in this section. Is there a substantial difference between
Bad Stuff in Cigarettes Refer to Data Set 5 in Appendix B.a. Use the paired data consisting of tar and nicotine. Based on the result, does there appear to be a significant correlation between cigarette tar and nicotine? If so, can researchers reduce their laboratory expenses by measuring only one
Buying a TV Audience The New York Post published the annual salaries (in millions)and the number of viewers (in millions), with results given below for Oprah Winfrey, David Letterman, Jay Leno, Kelsey Grammer, Barbara Walters, Dan Rather, James Gandolfini, and Susan Lucci, repsectively. Is there a
Correlation Between Heights and Weights of Supermodels Listed below are heights(in inches) and weights (in pounds) for supermodels Niki Taylor, Nadia Avermann, Claudia Schiffer, Elle MacPherson, Christy Turlington, Bridget Hall, Kate Moss, Valerie Mazza, and Kristy Hume.
Correlation Between Restaurant Bills and Tips Students of the author collected sample data consisting of amounts of restaurant bills and the corresponding tip amounts.The data are listed below. Use rank correlation to determine whether there is a correlation between the amount of the bill and the
Business School Rankings Business Week magazine ranked business schools two different ways. Corporate rankings were based on surveys of corporate recruiters, and graduate rankings were based on surveys of MBA graduates. The table below is based on the results for 10 schools. Is there a correlation
Correlation Between Salary and Physical Demand Exercise 3 includes paired salary and stress level ranks for 10 randomly selected jobs. The physical demands of the jobs were also ranked; the salary and physical demand ranks are given below (based on data from The Jobs Rated Almanac). Does there
Correlation Between Salary and Stress The accompanying table lists salary rankings and stress rankings for randomly selected jobs (based on data from The Jobs Rated Almanac). Does it appear that salary increases as stress increases?
Equivalent Tests Show that for the case of two samples, the Kruskal-Wallis test is equivalent to the Wilcoxon rank-sum test. This can be done by showing that for the case of two samples, the test statistic H equals the square of the test statistic z used in the Wilcoxon rank-sum test. Also note
Correcting the H Test Statistic for Ties In using the Kruskal-Wallis test, there is a correction factor that should be applied whenever there are many ties: Divide H by For each group of tied observations in the combined set of all sample data, calculate T 5 t 3 2 t, where t is the number of
Finding Values of the Test Statistic For three samples, each of size 5, find the largest and smallest possible values of the test statistic H.
Testing the Effect of Transforming the Sample Dataa. In general, how is the value of the test statistic H affected if a constant is added to(or subtracted from) each sample value?b. In general, how is the value of the test statistic H affected if each sample value is multiplied (or divided) by a
Home Run Distances Refer to Data Set 30 in Appendix B. Consider the home run distances to be samples randomly selected from populations. Use a 0.05 significance level to test the claim that the populations of distances of home runs hit by Barry Bonds, Mark McGwire, and Sammy Sosa are identical.
Do All Colors of M&Ms Weigh the Same? Refer to Data Set 19 in Appendix B. At the 0.05 significance level, test the claim that the weights of M&Ms are the same for each of the six different color populations. If it is the intent of Mars, Inc. to make the candies so that the different color
Laboratory Testing of Flammability of Children’s Sleepwear Flammability tests were conducted on children’s sleepwear. The Vertical Semirestrained Test was used, in which pieces of fabric were burned under controlled conditions. After the burning stopped, the length of the charred portion was
Testing for Skull-Breadth Differences in Different Times The accompanying values are measured maximum breadths of male Egyptian skulls from different epochs(based on data from Ancient Races of the Thebaid, by Thomson and RandallMaciver). Changes in head shape over time suggest that interbreeding
Is Solar Energy the Same Every Day? A student of the author lives in a home with a solar electric system. At the same time each day, she collected voltage readings from a meter connected to the system and the results are listed in the accompanying table.Use a 0.05 significance level to test the
Does the Weight of a Car Affect Head Injuries in a Crash? Data were obtained from car crash experiments conducted by the National Transportation Safety Administration. New cars were purchased and crashed into a fixed barrier at 35 mi h, and measurements were recorded for the dummy in the driver’s
Is Old Faithful Changing Over Time? Twelve different time intervals (in minutes)between eruptions of the Old Faithful geyser were recorded for each of the years 1951, 1985, and 1996. (The data are from geologist Rick Hutchinson and the National Park Service.) When Minitab is used with the
Marathon Times Running times for the males in the New York City marathon are listed in Data Set 8 in Appendix B. When those running times are partitioned into categories with ages of 21–29, 30–39, and 40 or older, the Minitab Kruskal-Wallis test results are as shown below. Do the running times
Finding Critical Values Assume that we have two treatments (A and B) that produce quantitative results, and we have only two observations for treatment A and two observations for treatment B. We cannot use the test statistic given in this section because both sample sizes do not exceed 10.a.
Testing the Anchoring Effect Randomly selected statistics students were given five seconds to estimate the value of a product of numbers with the results given in the accompanying table. (See the Cooperative Group Activities at the end of Chapter 2.) Is there sufficient evidence to support the
Are Severe Psychiatric Disorders Related to Biological Factors? One study used x-ray computed tomography (CT) to collect data on brain volumes for a group of patients with obsessive-compulsive disorders and a control group of healthy persons.The accompanying list shows sample results (in
Testing for Difference Between Times Depicting Alcohol Use and Tobacco Use Refer to Data Set 7 in Appendix B. Use only those movies that showed some use of tobacco or alcohol. (That is, ignore those movies with times of zero for both tobacco use and alcohol use.) Does there appear to be a
Testing for Drug Effectiveness Captopril is a drug designed to lower systolic blood pressure. When subjects were tested with this drug, their systolic blood pressure readings (in mm of mercury) were measured before and after the drug was taken, with the results given in the accompanying table. Is
Normal Approximation Error The Compulife.com company has hired 18 women among the last 54 new employees. Job applicants are about half men and half women, all of whom are qualified. Using a 0.01 significance level with the sign test, is there sufficient evidence to charge bias? Does the conclusion
Testing for Difference Between Forecast and Actual Temperatures Refer to Data Set 10 in Appendix B and use the actual high temperatures and the three-day forecast high temperatures. Does there appear to be a difference?
Testing for Median Time Interval for Old Faithful Geyser Refer to Data Set 13 in Appendix B. Test the claim that the intervals between eruptions of the Old Faithful geyser have a median greater than 77 min, which was the median about 30 years ago.
Testing for Median Amount of Domino Sugar in Packets Refer to Data Set 28 in Appendix B and use the sample data to test the claim that the median amount of sugar in the packets is equal to 3.5 oz. Does it appear that the sugar packets are being filled correctly?
Testing for Median Volume of Coke Cans Refer to Data Set 17 in Appendix B and use the volumes of regular Coke. Test the claim that cans of regular Coke have volumes with a median greater than 12 oz. Does it appear that the Coke cans are being filled correctly?
Nominal Data: Smoking and Nicotine Patches In one study of 71 smokers who tried to quit smoking with nicotine patch therapy, 41 were smoking one year after the treatment (based on data from “High-Dose Nicotine Patch Therapy,” by Dale et al., Journal of the American Medical Association, Vol.
Nominal Data: Survey of Voters In a survey of 1002 people, 701 said that they voted in the recent presidential election (based on data from ICR Research Group). Is there sufficient evidence to support the claim that the majority of people say that they voted in the election?
Testing for Median Underweight The Prince County Bottling Company supplies bottles of lemonade labeled 12 oz. When the Prince County Department of Weights and Measures tests a random sample of bottles, the amounts listed below are obtained.Using a 0.05 significance level, is there sufficient
Testing for a Median Body Temperature of 98.6°F A premed student in a statistics class is required to do a class project. Intrigued by the body temperatures in Data Set 4 Appendix B, she plans to collect her own sample data to test the claim that the mean body temperature is less than 98.6°F.
Testing for a Difference Between Reported and Measured Male Heights The table below lists matched pairs of measured heights of 12 male statistics students. Use a 0.05 significance level to test the claim that there is no difference between reported height and measured height.
Weights of Babies: Finding Probabilities In the United States, weights of newborn babies are normally distributed with a mean of 7.54 lb and a standard deviation of 1.09 lb (based on data from “Birth Weight and Prenatal Mortality,” by Wilcox, Skjaerven, Buekens, and Kiely, Journal of the
M&M Treatment The table below lists 60 SAT scores separated into categories according to the color of the M&M candy used as a treatment. The SAT scores are based on data from the College Board, and the M&M color element is based on author whimsy.a. Find the mean of the 20 SAT scores in each of the
Boston Rainfall Statistics Refer to the Boston rainfall amounts for Monday, as listed in Data Set 11 in Appendix B.a. Find the mean.b. Find the standard deviation.c. Find the 5-number summary.d. Identify any outliers.e. Construct a histogram.f. Assume that you want to test the null hypothesis that
Auto Pollution The accompanying table lists the amounts of greenhouse gases emitted by different cars in one year. (See Data Set 22 in Appendix B.) The Minitab display results from this table.a. Assuming that there is no interaction effect, is there sufficient evidence to support the claim that
Effect of Major Assume that estimated lengths are not affected by an interaction between gender and major. Is there sufficient evidence to support the claim that estimated length is affected by major?
Effect of Gender Assume that estimated lengths are not affected by an interaction between gender and major. Is there sufficient evidence to support the claim that estimated length is affected by gender?
Interaction Effect Test the null hypothesis that the estimated lengths are not affected by an interaction between gender and major.
Transformations of Data Assume that two-way ANOVA is used to analyze sample data consisting of more than one entry per cell. How are the ANOVA results affected in each of the following cases?a. The same constant is added to each sample value.b. Each sample value is multiplied by the same nonzero
Car Fuel Consumption The following table lists highway fuel consumption amounts(in mi gal) from Data Set 22 in Appendix B. Assume that fuel consumption amounts are not affected by an interaction between the type of transmission (manual or automatic) and the number of cylinders. Are fuel consumption
Pulse Rates The following table lists pulse rates from Data Set 1 in Appendix B. Are pulse rates affected by an interaction between gender and age? Are pulse rates affected by gender? Are pulse rates affected by age?
Hearing Tests: Effect of Word List Assuming that there is no effect on hearing test scores from an interaction between subject and list, is there sufficient evidence to support the claim that the choice of word list has an effect on the hearing test score?
Hearing Tests: Effect of Subject Assuming that there is no effect on hearing test scores from an interaction between subject and list, is there sufficient evidence to support the claim that the choice of subject has an effect on the hearing test score? Interpret the result by explaining why it
Effect of Type of SAT Test Assume that SAT scores are not affected by an interaction between gender and the type of test (verbal math). Is there sufficient evidence to support the claim that the type of test (verbal math) has an effect on SAT scores?
Effect of Gender Assume that SAT scores are not affected by an interaction between gender and the type of test (verbal math). Is there sufficient evidence to support the claim that gender has an effect on SAT scores?
Interaction Effect Test the null hypothesis that SAT scores are not affected by an interaction between gender and test (verbal math). What do you conclude?
Effect of Age Refer to the Minitab display and assume that the amounts of DDT in the falcons are not affected by an interaction between site and age. Is there sufficient evidence to support the claim that age has an effect on the amount of DDT?
Effect of Site Refer to the Minitab display and assume that the amounts of DDT in the falcons are not affected by an interaction between site and age. Is there sufficient evidence to support the claim that site has an effect on the amount of DDT?
Interaction Effect Refer to the Minitab display and test the null hypothesis that the amounts of DDT are not affected by an interaction between site and age. What do you conclude?
Why Not Use Two-Way ANOVA? Why can’t we use the method of two-way analysis of variance with two-way tables described in Section 10-3?
Interaction Effect Assume that two-way analysis of variance reveals that there is a significant effect from an interaction between two factors. Why should we not proceed to test the effect from the row factor?
Why Not One-Way ANOVA? The given Minitab display results from measured amounts of DDT in falcons partitioned into nine cells according to one factor of location and another factor of age of the falcon. Each cell includes three DDT measurements. Why can’t we conduct a thorough analysis of the data
Meaning of Two-Way ANOVA The method of this section is referred to as two-way analysis of variance, or two-way ANOVA. Why is the term two-way used? Why is the term analysis of variance used?
Equivalent Tests In this exercise you will verify that when you have two sets of sample data, the t test for independent samples and the ANOVA method of this section are equivalent. Refer to the readability measurements in Table 11-1, but use only the data for Clancy and Rowling. The original data
Using t Test Five independent samples of 50 values each are randomly drawn from populations that are normally distributed with equal variances. We wish to test the claim that m1 5 m2 5 m3 5 m4 5 m5.a. If we used only the methods given in Section 8-3, we would test the individual claims m1 5 m2, m1
Secondhand Smoke in Different Groups Refer to Data Set 6 in Appendix B. Use a 0.05 significance level to test the claim that the mean cotinine level is different for these three groups: nonsmokers who are not exposed to environmental tobacco smoke, nonsmokers who are exposed to tobacco smoke, and
Sugar in Cereal Refer to Data Set 16 in Appendix B and combine the sugar amounts for shelves 3 and 4, which are the two highest shelves. Use a 0.05 significance level to test the null hypothesis that the mean sugar amounts on the different shelves are all the same. What do the results suggest about
Home Run Distances Refer to Data Set 30 in Appendix B. Use a 0.05 significance level to test the claim that the home runs hit by Barry Bonds, Mark McGwire, and Sammy Sosa have mean distances that are not all the same. Do the home run distances explain the fact that as of this writing, Barry Bonds
Mean Weights of M&Ms Refer to Data Set 19 in Appendix B. At the 0.05 significance level, test the claim that the mean weight of M&Ms is the same for each of the six different color populations. If it is the intent of Mars, Inc. to make the candies so that the different color populations have the
Solar Energy in Different Weather A student of the author lives in a home with a solar electric system. At the same time each day, she collected voltage readings from a meter connected to the system and the results are listed in the accompanying table.Use a 0.05 significance level to test the claim
Archaeology: Skull Breadths from Different Epochs The values in the table are measured maximum breadths of male Egyptian skulls from different epochs (based on data from Ancient Races of the Thebaid, by Thomson and Randall-Maciver). Changes in head shape over time suggest that interbreeding
Chest Deceleration in a Car Crash The chest deceleration data (g) are given below.Use a 0.05 significance level to test the null hypothesis that the different weight categories have the same mean. Do the data suggest that larger cars are safer?
Head Injury in a Car Crash The head injury data (in hic) are given below. Use a 0.05 significance level to test the null hypothesis that the different weight categories have the same mean. Do the data suggest that larger cars are safer?Subcompact: 681 428 917 898 420 Compact: 643 655 442 514 525
Systolic Blood Pressure in Different Age Groups A random sample of 40 women is partitioned into three categories with ages of below 20, 20 through 40, and over 40.The systolic blood pressure levels are obtained from Data Set 1 in Appendix B. The analysis of variance results obtained from Minitab
Marathon Times A random sample of males who finished the New York marathon is partitioned into three categories with ages of 21–29, 30–39, and 40 or over. The times(in seconds) are obtained from Data Set 8 in Appendix B. The analysis of variance results obtained from Excel are shown below.a.
Fabric Flammability Tests in Different Laboratories Flammability tests were conducted on children’s sleepwear. The Vertical Semirestrained Test was used, in which pieces of fabric were burned under controlled conditions. After the burning stopped, the length of the charred portion was measured
Readability of Authors The Chapter Problem uses the Flesch Reading Ease scores for randomly selected pages from books by Tom Clancy, J. K. Rowling, and Leo Tolstoy.If the Flesch-Kincaid Grade Level scores are used instead (see Data Set 14 in Appendix B), the analysis of variance results from
Testing for Equality of Means Assume that in Table 10-8, the letters A, B, C, and D represent different versions of the same test of reasoning. The x-scores were obtained by four randomly selected men and the y-scores were obtained by four randomly selected women. Test the claim that men and women
Testing for Effectiveness of Training Assume that Table 10-8 lists test scores for four people, where the x-score is from a pretest taken before a training session on memory improvement and the y-score is from a posttest taken after the training. Test the claim that the training session is
Testing for a Relationship Assume that Table 10-8 lists test scores for four people, where the x-score is from a test of memory and the y-score is from a test of reasoning.Test the claim that there is a relationship between the x- and y-scores.
Testing for Equal Proportions Using the same assumptions as in Exercise 2, test the claim that men and women choose the different answers in the same proportions.
Finding Probability Assume that in Table 10-8, the letters A, B, C, and D represent the choices on the first question of a multiple-choice quiz. Also assume that x represents men and y represents women and that the table entries are frequency counts, so 66 men chose answer A, 77 women chose answer
Finding Statistics Assume that in Table 10-8, the row and column titles have no meaning so that the table contains test scores for eight randomly selected prisoners who were convicted of removing labels from pillows. Find the mean, median, range, variance, standard deviation, and 5-number summary.
Testing for Independence Between Early Discharge and Rehospitalization of Newborn Is it safe to discharge newborns from the hospital early after their births? The accompanying table shows results from a study of this issue. Use a 0.05 significance level to test the claim that whether the newborn
Is Drinking Independent of Type of Crime? The accompanying table lists sample data that statistician Karl Pearson used in 1909. Does the type of crime appear to be related to whether the criminal drinks or abstains? Are there any crimes that appear to be associated with drinking?
Do Gunfire Deaths Occur More Often on Weekends? When Time magazine tracked U.S. deaths by gunfire during a one-week period, the results shown in the accompanying table were obtained. At the 0.05 significance level, test the claim that gunfire death rates are the same for the different days of the
Call Center Data The table lists the calls received by a call center during one week in a recent year. (The data are from a large U.S. electronics producer that wishes to remain anonymous.) Use a 0.05 significance level to test the claim that calls are uniformly distributed over the days of the
Using Yates’ Correction for Continuity The chi-square distribution is continuous, whereas the test statistic used in this section is discrete. Some statisticians use Yates’correction for continuity in cells with an expected frequency of less than 10 or in all cells of a contingency table with
Exercise and Smoking A study of the effects of exercise by women included results summarized in the table (based on data from “Physical Activity and Coronary Heart Disease in Women” by Lee, Rexrode, Cook, Manson, and Buring, Journal of the American Medical Association, Vol. 285, No. 11).
Clinical Test of Lipitor The cholesterol-reducing drug Lipitor consists of atorvastatin calcium, and results summarizing headaches as an adverse reaction in clinical tests are given in the table (based on data from Parke-Davis). Using a 0.05 significance level, test the claim that getting a
Is the Home Field Advantage Independent of the Sport? Winning team data were collected for teams in different sports, with the results given in the accompanying table.Use a 0.10 significance level to test the claim that home visitor wins are independent of the sport. Given that among the four
Is Sentence Independent of Plea? Many people believe that criminals who plead guilty tend to get lighter sentences than those who are convicted in trials. The accompanying table summarizes randomly selected sample data for San Francisco defendants in burglary cases. All of the subjects had prior
Is Seat Belt Use Independent of Cigarette Smoking? A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the given table. Test the claim that the amount of smoking is independent of seat-belt use. A plausible theory is that people who smoke more are less
Crime and Strangers The accompanying table lists survey results obtained from a random sample of different crime victims. At the 0.05 significance level, test the claim that the type of crime is independent of whether the criminal is a stranger. How might the results affect the strategy police
Firearm Training and Safety Does firearm training result in safer practices by gun owners? In one study, randomly selected subjects were surveyed with the results given in the accompanying table. Use a 0.05 significance level to test the claim that formal firearm training is independent of how
Survey Refusals and Age Bracket A study of people who refused to answer survey questions provided the randomly selected sample data shown in the table. At the 0.01 significance level, test the claim that the cooperation of the subject (response or refusal) is independent of the age category. Does

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