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elementary statistics
Elementary Statistics 9th Edition Mario F. Triola - Solutions
Is Scanner Accuracy the Same for Specials? In a study of store checkout scanning systems, samples of purchases were used to compare the scanned prices to the posted prices. The accompanying table summarizes results for a sample of 819 items. When stores use scanners to check out items, are the
Occupational Hazards Use the data in the table to test the claim that occupation is independent of whether the cause of death was homicide. The table is based on data from the U.S. Department of Labor, Bureau of Labor Statistics. Does any particular occupation appear to be most prone to homicides?
Smoking in China The table below summarizes results from a survey of males aged 15 or older living in the Minhang District of China (based on data from “Cigarette Smoking in China” by Gong, Koplan, Feng, et al., Journal of the American Medical Association, Vol. 274, No. 15). Using a 0.05
No Smoking Repeat Exercise 8 after including the additional data shown in the table.
No Smoking The accompanying table summarizes successes and failures when subjects used different methods in trying to stop smoking. The determination of smoking or not smoking was made five months after the treatment was begun, and the data are based on results from the Centers for Disease Control
Fear of Flying Gender Gap The Marist Institute for Public Opinion conducted a poll of 1014 adults, 48% of whom were men. The poll results show that 12% of the men and 33% of the women fear flying. After constructing a contingency table that summarizes the data in the form of frequency counts, use a
Testing for Discrimination In the judicial case United States v. City of Chicago, fair employment practices were challenged. A minority group (group A) and a majority group (group B) took the Fire Captain Examination. Assume that the study began with predetermined sample sizes of 24 minority
Testing Influence of Gender Table 10-7 summarizes data for male survey subjects, but the accompanying table summarizes data for a sample of women. Using a 0.01 significance level, and assuming that the sample sizes of 800 men and 400 women are predetermined, test the claim that the proportions of
Accuracy of Polygraph Tests The data in the accompanying table summarize results from tests of the accuracy of polygraphs (based on data from the Office of Technology Assessment). Use a 0.05 significance level to test the claim that whether the sub ject lies is independent of the polygraph
E-Mail and Privacy Workers and senior-level bosses were asked if it was seriously unethical to monitor employee e-mail, and the results are summarized in the table(based on data from a Gallup poll). Use a 0.05 significance level to test the claim that the response is independent of whether the
Is there Racial Profiling? Racial profiling is the controversial practice of targeting someone for criminal behavior on the basis of the person’s race, national origin, or ethnicity. The accompanying table summarizes results for randomly selected drivers stopped by police in a recent year (based
Testing Goodness-of-Fit with a Normal Distribution An observed frequency distribution of sample IQ scores is as follows:a. Assuming a normal distribution with m 5 100 and s 5 15, use the methods given in Chapter 5 to find the probability of a randomly selected subject belonging to each class. (Use
Testing Goodness-of-Fit with a Binomial Distribution An observed frequency distribution is as follows:a. Assuming a binomial distribution with n 5 3 and p 5 1 3, use the binomial probability formula to find the probability corresponding to each category of the table.b. Using the probabilities found
Equivalent Test In this exercise we will show that a hypothesis test involving a multinomial experiment with only two categories is equivalent to a hypothesis test for a proportion (Section 7-3). Assume that a particular multinomial experiment has only two possible outcomes, A and B, with observed
Detecting Altered Experimental Data When Gregor Mendel conducted his famous hybridization experiments with peas, it appears that his gardening assistant knew the results that Mendel expected, and he altered the results to fit Mendel’s expectations.Subsequent analysis of the results led to the
Testing Effects of Outliers In conducting a test for the goodness-of-fit as described in this section, does an outlier have much of an effect on the value of the x2 test statistic? Test for the effect of an outlier by repeating Exercise 6 after changing the frequency for the right rear tire from 6
Do World War II Bomb Hits Fit a Poisson Distribution? 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. In Section 4-5 we presented an example and included a table of actual frequencies of hits and the frequencies expected
Author’s Check Amounts and Benford’s Law Figure 10-6(b) illustrates the observed frequencies of the leading digits from the amounts of the last 200 checks that the author wrote. The observed frequencies of those leading digits are listed below. Using a 0.05 significance level, test the claim
Distribution of Digits in the Rational Number 22 7 The number 22 7 is similar to p in the sense that they both require an infinite number of decimal places. However, 22 7 is a rational number because it can be expressed as the ratio of two integers, whereas p cannot. When rational numbers such as
Distribution of Digits in the Irrational Number Pi The number p is an irrational number with the property that when we try to express it in decimal form, it requires an infinite number of decimal places and there is no pattern of repetition. In the decimal representation of p, the first 100 digits
Car Crashes and Age Brackets Among drivers who have had a car crash in the last year, 88 are randomly selected and categorized by age, with the results listed in the accompanying table. If all ages have the same crash rate, we would expect (because of the age distribution of licensed drivers) the
M&M Candies Mars, Inc. claims that its M&M plain candies are distributed with the following color percentages: 30% brown, 20% yellow, 20% red, 10% orange, 10%green, and 10% blue. Refer to Data Set 19 in Appendix B and use the sample data to test the claim that the color distribution is as claimed
Are Violent Crimes Distributed Uniformly? Based on data from the Federal Bureau of Investigation, violent crimes in a recent year occurred with the distribution given in the accompanying table. Violent crimes include murder, nonnegligent manslaughter, rape, robbery, and aggravated assault. The
Are the Win 4 Numbers Random? Refer to Data Set 26 in Appendix B and use the 160 digits that were selected in New York State’s Win 4 lottery game. Using a 0.05 significance level, test the claim that those digits are selected in such a way that the ten possible digits are all equally likely. Does
Measuring Pulse Rates An example in this section was based on the principle that when certain quantities are measured, the last digits tend to be uniformly distributed, but if they are estimated or reported, the last digits tend to have disproportionately more 0s or 5s. Refer to Data Set 1 in
Post Position and Winning Horse Races Many people believe that when a horse races, it has a better chance of winning if its starting line-up position is closer to the rail on the inside of the track. The starting position of 1 is closest to the inside rail, followed by position 2, and so on. The
Grade and Seating Location Do “A” students tend to sit in a particular part of the classroom? The author recorded the locations of the students who received grades of A, with these results: 17 sat in the front, 9 sat in the middle, and 5 sat in the back of the classroom. Is there sufficient
Testing for Uniformly Distributed Industrial Accidents A study was made of 147 industrial accidents that required medical attention. Among those accidents, 31 occurred on Monday, 42 on Tuesday, 18 on Wednesday, 25 on Thursday, and 31 on Friday (based on results from “Counted Data CUSUM’s,” by
Are DWI Fatalities the Result of Weekend Drinking? Many people believe that fatal DWI crashes occur because of casual drinkers who tend to binge on Friday and Saturday nights, whereas others believe that fatal DWI crashes are caused by people who drink every day of the week. In a study of fatal car
Do Car Crashes Occur on Different Days with the Same Frequency? It is a common belief that more fatal car crashes occur on certain days of the week, such as Friday or Saturday. A sample of motor vehicle deaths for a recent year in Montana is randomly selected. The numbers of fatalities for the
Flat Tire and Missed Class A classic tale involves four car-pooling students who missed a test and gave as an excuse a flat tire. On the makeup test, the instructor asked the students to identify the particular tire that went flat. If they really didn’t have a flat tire, would they be able to
Loaded Die 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, 31, 42, 40, 28, 32. Use a 0.05 significance level to test the claim that the outcomes
Testing a Slot Machine The author purchased a slot machine (Bally Model 809), and tested it by playing it 1197 times. When testing the claim that the observed outcomes agree with the expected frequencies, a test statistic of x2 5 8.185 was obtained. There are ten different categories of outcome,
Testing Fairness of Roulette Wheel The author observed 500 spins of a roulette wheel at the Mirage Resort and Casino. (To the IRS: Isn’t that Las Vegas trip now a tax deduction?) For each spin, the ball can land in any one of 38 different slots that are supposed to be equally likely. When
Assume that we want to use a 0.05 significance level to test the claim that the five categories have proportions of 0.2, 0.2, 0.2, 0.3, and 0.1, respectively.a. What is the null hypothesis?b. What are the expected frequencies for the five categories?c. What is the value of the test statistic?d.
Testing for Categories with Different Proportions Here are the observed frequencies from five categories: 9, 8, 13, 14,
Assume that we want to use a 0.05 significance level to test the claim that the four categories are all equally likely.a. What is the null hypothesis?b. What is the expected frequency for each of the four categories?c. What is the value of the test statistic?d. What is the critical value?e. What do
Testing for Equally Likely Categories Here are the observed frequencies from four categories: 5, 6, 8,
E-Mail and Privacy Refer to the sample data given in Exercise 7 and construct a 90%confidence interval estimate of the difference between the two population proportions. Is there a substantial gap between the employees and bosses?
Exercise and Coronary Heart Disease In a study of women and coronary heart disease, the following sample results were obtained: Among 10,239 women with a low level of physical activity (less than 200 kcal wk), there were 101 cases of coronary heart disease. Among 9877 women with physical activity
Exercise and Coronary Heart Disease Refer to the sample data in Exercise 9 and use a 0.05 significance level to test the claim that the rate of coronary heart disease is higher for women with the lower levels of physical activity. What does the conclusion suggest?
Instant Replay in Football In the 2000 football season, 247 plays were reviewed by officials using instant video replays, and 83 of them resulted in reversal of the original call. In the 2001 football season, 258 plays were reviewed and 89 of them were reversed (based on data from “Referees Turn
Effectiveness of Smoking Bans The Joint Commission on Accreditation of Healthcare Organizations mandated that hospitals ban smoking by 1994. In a study of the effects of this ban, subjects who smoke were randomly selected from two different populations. Among 843 smoking employees of hospitals with
Testing Effectiveness of Vaccine In a USA Today article about an experimental nasal spray vaccine for children, the following statement was presented: “In a trial involving 1602 children only 14 (1%) of the 1070 who received the vaccine developed the flu, compared with 95 (18%) of the 532 who got
Color Blindness in Men and Women In a study of red green color blindness, 500 men and 2100 women are randomly selected and tested. Among the men, 45 have red green color blindness. Among the women, 6 have red green color blindness(based on data from USA Today).a. Is there sufficient evidence to
Seat Belts and Hospital Time A study was made of 413 children who were hospitalized as a result of motor vehicle crashes. Among 290 children who were not using seat belts, 50 were injured severely. Among 123 children using seat belts, 16 were injured severely (based on data from “Morbidity Among
Drinking and Crime Karl Pearson, who developed many important concepts in statistics, collected crime data in 1909. Of those convicted of arson, 50 were drinkers and 43 abstained. Of those convicted of fraud, 63 were drinkers and 144 abstained. Use a 0.01 significance level to test the claim that
Interpreting a Computer Display A U.S. Department of Justice report (NCJ-156831)included the claim that “in spouse murder cases, wife defendants were less likely to be convicted than husband defendants.” Sample data consisted of 277 convictions among 318 husband defendants, and 155 convictions
Effectiveness of Salk Vaccine for Polio In initial tests of the Salk vaccine, 33 of 200,000 vaccinated children later developed polio. Of 200,000 children vaccinated with a placebo, 115 later developed polio. The TI-83 Plus calculator display is shown here. At the 0.01 significance level, test the
Airline Load Factor In a recent year, Southwest Airlines had 3,131,727 aircraft seats available on all of its flights, and 2,181,604 of them were occupied by passengers.America West had 2,091,859 seats available, and 1,448,255 of them were occupied.The percentage of seats occupied is called the
Attitudes Toward Marriage In a Time CNN survey, 24% of 205 single women said that they “definitely want to get married.” In the same survey, 27% of 260 single men gave that same response. Construct a 99% confidence interval estimate of the difference between the proportions of single women and
Attitudes Toward Marriage Refer to the same sample data in Exercise 21 and use a 0.01 significance level to test the claim that there is a difference between the proportion of men and the proportion of women who definitely want to get married. Does there appear to be a difference?
Violent Crime and Age Group The newly appointed head of the state mental health agency claims that a smaller proportion of the crimes committed by persons younger than 21 years of age are violent crimes (when compared to the crimes committed by persons 21 years of age or older). Of 2750 randomly
Testing Laboratory Gloves The New York Times ran an article about a study in which Professor Denise Korniewicz and other Johns Hopkins researchers subjected laboratory gloves to stress. Among 240 vinyl gloves, 63% leaked viruses. Among 240 latex gloves, 7% leaked viruses. At the 0.005 significance
Written Survey and Computer Survey In a study of 1700 teens aged 15–19, half were given written surveys and half were given surveys using an anonymous computer program. Among those given the written surveys, 7.9% say that they carried a gun within the last 30 days. Among those given the computer
Adverse Drug Reactions The drug Viagra has become quite well known, and it has had a substantial economic impact on its producer, Pfizer Pharmaceuticals. In prelim-inary tests for adverse reactions, it was found that when 734 men were treated with Viagra, 16% of them experienced headaches.
Poll Refusal Rate Professional pollsters are becoming concerned about the growing rate of refusals among potential survey subjects. In analyzing the problem, there is a need to know if the refusal rate is universal or if there is a difference between the rates for central-city residents and those
Home Field Advantage When games were sampled from throughout a season, it was found that the home team won 127 of 198 professional basketball games, and the home team won 57 of 99 professional football games (based on data from “Predicting Professional Sports Game Outcomes from Intermediate Game
Alcohol and Tobacco in Children’s Movies Test the claim that the proportion of 25 of 50 randomly selected children’s movies showing some use of alcohol is significantly less than the sample proportion of 28 of 50 other such movies showing some use of tobacco. Do the results apply to Data Set 7?
Health Survey Refer to Data Set 1 in Appendix B and use the sample data to test the claim that the proportion of men over the age of 30 is equal to the proportion of women over the age of 30.8-2 Beyond the Basics
Interpreting Overlap of Confidence Intervals In the article “On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals” by Schenker and Gentleman (The American Statistician, Vol. 55, No. 3), the authors consider sample data in this statement:
Equivalence of Hypothesis Test and Confidence Interval Two different simple random samples are drawn from two different populations. The first sample consists of 20 people with 10 having a common attribute. The second sample consists of 2000 people with 1404 of them having the same common
Same Proportions with Larger Samples This section used the sample data in Table 8-1 to test the claim that p1 5 p2 and to construct a confidence interval estimate of p1 2 p2. How are the results affected if the sample data in Table 8-1 are modified so that p1 becomes 240 2000 instead of 24 200, and
Testing for Constant Difference To test the null hypothesis that the difference between two population proportions is equal to a nonzero constantc, use the test statistic As long as n1 and n2 are both large, the sampling distribution of the test statistic z will be approximately the standard normal
Transitivity of Hypothesis Tests Sample data are randomly drawn from three independent populations, each of size 100. The sample proportions are 1 5 40 100, 2 5 30 100, and 3 5 20 100.a. At the 0.05 significance level, test H0: p1 5 p2.b. At the 0.05 significance level, test H0: p2 5 p3.c. At the
Determining Sample Size The sample size needed to estimate the difference between two population proportions to within a margin of error E with a confidence level of 1 2 a can be found as follows. In the expression replace n1 and n2 by n (assuming that both samples have the same size) and replace
Confidence Interval for Effects of Marijuana Use on College Students Refer to the sample data used in Exercise 5 and construct a 98% confidence interval for the difference between the two population means. Does the confidence interval include zero?What does the confidence interval suggest about the
Confidence Interval for Bipolar Depression Treatment In clinical experiments involving different groups of independent samples, it is important that the groups be similar in the important ways that affect the experiment. In an experiment designed to test the effectiveness of paroxetine for treating
Hypothesis Test for Bipolar Depression Treatment Refer to the sample data in Exercise 7 and use a 0.05 significance level to test the claim that the treatment group and placebo group come from populations with the same mean. What does the result of the hypothesis test suggest about paroxetine as a
Hypothesis Test for Magnet Treatment of Pain People spend huge sums of money(currently around $5 billion annually) for the purchase of magnets used to treat a wide variety of pains. Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured
Confidence Interval for Magnet Treatment of Pain Refer to the sample data from Exercise 9 and construct a 90% confidence interval estimate of the difference between the mean reduction in pain for those treated with magnets and the mean reduction in pain for those given a sham treatment. Based on
Inferences from Samples of Regular Coke and Diet Coke Using Data Set 17 in Appendix B, we find the sample statistics for the weights (in pounds) of regular Coke and diet Coke as listed in the margin.a. Use a 0.01 significance level to test the claim that cans of regular Coke and diet Coke have the
Cigarette Filters and Nicotine Refer to the sample results listed in the margin for the measured nicotine contents of randomly selected filtered and nonfiltered king-size cigarettes. All measurements are in milligrams, and the data are from the Federal Trade Commission.a. Use a 0.05 significance
Hypothesis Test for Identifying Psychiatric Disorders Are severe psychiatric disorders related to biological factors that can be physically observed? 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
Confidence Interval for Identifying Psychiatric Disorders Refer to the sample data in Exercise 13 and use a 0.01 significance level to test the claim that there is a difference between the two population means. Based on the result, does it seem that obsessivecompulsive disorders have a biological
Confidence Interval for Effects of Alcohol An experiment was conducted to test the effects of alcohol. The errors were recorded in a test of visual and motor skills for a treatment group of people who drank ethanol and another group given a placebo. The results are shown in the accompanying table
Hypothesis Test for Effects of Alcohol Refer to the sample data in Exercise 15 and use a 0.05 significance level to test the claim that there is a difference between the treatment group and control group. If there is a significant difference, can we conclude that the treatment causes a decrease in
Hypothesis Test for Eyewitness Accuracy of Police Does stress affect the recall ability of police eyewitnesses? This issue was studied in an experiment that tested eyewitness memory a week after a nonstressful interrogation of a cooperative suspect and a stressful interrogation of an uncooperative
Confidence Interval for Eyewitness Accuracy of Police Using the sample data from Exercise 17, construct a 98% confidence interval estimate of the difference between the two population means. Does the result support the claim in the article that “stress decreased the amount recalled”? Why or why
Queen Mary Stowaways Data Set 15 in Appendix B lists the ages of stowaway passengers on westbound and eastbound trips of the Queen Mary. When Excel is used with those two sets of ages, the results are as shown below. Is there a significant difference between the ages of stowaway passengers on
Reading Levels When a TI-83 Plus calculator is used with the Flesch reading ease scores for Tom Clancy’s The Bear and the Dragon and J. K. Rowling’s Harry Potter and the Sorcerer’s Stone, the accompanying results are obtained. (The sample data are listed in Data Set 14 in Appendix B.) Is
Tar and Cigarettes Refer to the sample data listed below and use a 0.05 significance level to test the claim that the mean amount of tar in filtered king-size cigarettes is less than the mean amount of tar in nonfiltered king-size cigarettes. All measurements are in milligrams, and the data are
Blanking Out on Tests Many students have had the unpleasant experience of panicking on a test because the first question was exceptionally difficult. The arrangement of test items was studied for its effect on anxiety. The following scores are measures of“debilitating test anxiety,” which most
Effects of an Outliera. Refer to Exercise 19 and include an outlier consisting of a 90-year-old stowaway on a westbound crossing of the Queen Mary. Is the hypothesis test dramatically affected by the presence of the outlier?b. Refer to Exercise 19 and include an outlier consisting of a
Effects of Units of Measurement How are the results of Exercise 12 affected if the amounts of nicotine are all converted from milligrams to ounces? In general, does the choice of the scale affect the conclusions about equality of the two population means, and does the choice of scale affect the
Verifying a Property of Variancesa. Find the variance for this population of x values: 5, 10, 15. (See Section 2-5 for the variance s2 of a population.)b. Find the variance for this population of y values: 1, 2, 3.c. List the population of all possible differences x 2 y, and find the variance of
Effect of No Variation in Sample An experiment was conducted to test the effects of alcohol. The breath alcohol levels were measured for a treatment group of people who drank ethanol and another group given a placebo. The results are given in the accompanying table. Use a 0.05 significance level to
Calculating Degrees of Freedom How is the number of degrees of freedom for Exercises 13 and 14 affected if Formula 8-1 is used instead of selecting the smaller of n1 2 1 and n2 2 1? If Formula 8-1 is used for the number of degrees of freedom instead of the smaller of n1 2 1 and n2 2 1, how are the
Before After Treatment Results 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
Effectiveness of Hypnotism in Reducing Pain A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for randomly selected subjects are given in the accompanying table (based on “An Analysis of Factors That Contribute to the Efficacy of Hypnotic Analgesia,”
Measuring Intelligence in Children Mental measurements of young children are often made by giving them blocks and telling them to build a tower as tall as possible.One experiment of block building was repeated a month later, with the times (in seconds) listed in the accompanying table (Based on
Testing Corn Seeds In 1908, William Gosset published the article “The Probable Error of a Mean” under the pseudonym of “Student” (Biometrika, Vol. 6, No. 1). He included the data listed below for two different types of corn seed (regular and kiln dried) that were used on adjacent plots of
Parent’s Heights Refer to Data Set 2 in Appendix B and use only the data corresponding to male children. Use the paired data consisting of the mother’s height and the father’s height.a. Use a 0.01 significance level to test the claim that mothers of male children are shorter than the
Treating Motion Sickness The following Minitab display resulted from an experiment in which 10 subjects were tested for motion sickness before and after taking the drug astemizole. The Minitab data column C3 consists of differences in the number of head movements that the subjects could endure
Dieting: Interpreting Calculator Display Researchers obtained weight loss data from a sample of dieters using the New World Athletic Club facilities. The before and after weights are recorded, then the differences (before 2 after) are computed. The TI-83 Plus calculator results are shown for a test
Self-Reported and Measured Weights of Males Refer to the Excel display of the results obtained when testing the claim that there is no difference between self-reported weights and measured weights of males aged 12–16. Is there sufficient evidence to support the claim that there is a difference?
Self-Reported and Measured Heights of Male Statistics Students Male statistics students were given a survey that included a question asking them to report their height in inches. They weren’t told that their height would be measured, but heights were accurately measured after the survey was
Morning and Night Body Temperatures Refer to Data Set 4 in Appendix B. Use the paired data consisting of body temperatures of women at 8:00 AM and at 12:00 AM on Day 2.a. Construct a 95% confidence interval for the mean difference of 8 AM temperatures minus 12 AM temperatures.b. Using a 0.05
Tobacco and Alcohol in Children’s Movies Refer to Data Set 7 in Appendix B. Use the paired data consisting of times that the movies showed tobacco use and the times that they showed alcohol use.a. Is there sufficient evidence to conclude that the times are different?b. Construct a 99% confidence
Forecast and Actual Temperatures The examples in this section used only five pairs of sample data so that the calculations would be easy. Refer to Data Set 10 in Appendix B and use all of the actual low temperatures and the low temperatures that were forecast five days earlier.a. Using a 0.05
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