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Elementary Statistics 10th Edition Mario F. Triola - Solutions

Weight Loss from Different Diets In a test of the Atkins, Zone, Weight Watchers, and Ornish weight loss programs, 160 subjects followed the diet programs, with 40 subjects using each diet. They were weighed one year after being on the diet, and the ANOVA results from Excel are given below (based on
Weights of Poplar Trees The Chapter Problem uses the weights of poplar trees for Year 1 and Site 1. (See Data Set 7 in Appendix B.) If we use the weights for Year 2 and Site 1, the analysis of variance results from the TI-83 84 Plus calculator are as shown in the accompanying display. Assume that
Weights of Poplar Trees We noted in the Chapter Problem that the weight of 1.34 kg appears to be an outlier. If we delete that value, the STATDISK results are as shown below.a. What is the null hypothesis?b. What is the alternative hypothesis?c. Identify the value of the test statistic.d. Identify
Comparing Majors A student at the College of Newport administers a test of abstract reasoning to randomly selected English, mathematics, and science majors at her college.She then uses analysis of variance with the sample data and concludes that the means are not all equal. Can she conclude that in
Between Within What is variance between samples, and what is variance within samples?
Treatment In the context of analysis of variance, what is a treatment? In this context, is the meaning the same as in general usage of the word “treatment”?
ANOVA What is one-way analysis of variance, and what is it used for?
Do the leading digits conform to Benford’s law described in the Chapter Problem?When testing for goodness-of-fit with the proportions expected with Benford’s law, it is necessary to combine categories because not all expected values are at least 5. Use one category with leading digits of 1, a
Testing for Effectiveness of Training Assume that Table 11-11 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 has no
Testing for a Relationship Assume that Table 11-11 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 linear correlation between the x- and y-scores.
Finding Probability Assume that in Table 11-11, 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 85 men chose answer A, 80 women chose answer
Finding Statistics Assume that in Table 11-11, 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.
Comparing Treatments Two different creams are used to treat subjects with poison ivy irritation on both hands. Each subject is given a treatment of Ivy Ease on one hand while their other hand is treated with a placebo. The sample results are summarized in the table below. Use a 0.05 significance
Crime and Strangers The accompanying table lists survey results obtained from a random sample of different crime victims (based on data from the U.S. Department of Justice). At the 0.05 significance level, test the claim that the type of crime is independent of whether the criminal is a stranger.
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
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
Checking Requirements The methods of testing for goodness-of-fit and the methods of testing for independence between two variables used for a contingency table require that all expected frequencies must be at least 5. Can those methods be used if there is a cell with an observed frequency count
Chi-Square Distribution This chapter presented different methods involving application of the chi-square distribution. Which of the following properties of a chi-square distribution are true?a. Values of a chi-square test statistic are always positive or zero, but never negative.b. A chi-square
Conducting a Survey A student conducts a research project by asking 200 classmates if they have had a credit card stolen. She constructs a contingency table with row categories of gender (male female) and column categories of response (yes, no, refused to answer). She uses the methods of Section
Categorical Data This chapter introduced a few different methods for the analysis of categorical data. What are categorical data?
Small Sample Case The requirements for McNemar’s test include the condition that b 1 c $ 10 so that the distribution of the test statistic can be approximated by the chisquare distribution. Refer to the example in this section and replace the table data with the values given below. McNemar’s
Using Common Sense Consider the table given below, and use a 0.05 significance level.a. What does McNemar’s test suggest about the effectiveness of the treatment?b. The values of a and d are not used in the calculations, but what does common sense suggest if a 5 5000 and d 5 4000?
Correction for Continuity The test statistic given in this section includes a correction for continuity. The test statistic given below does not include the correction for continuity, and it is sometimes used as the test statistic for McNemar’s test. Refer to the example in this section, find the
Testing a Treatment In the article “Eradication of Small Intestinal Bacterial Overgrowth Reduces Symptoms of Irritable Bowel Syndrome” (Pimentel, Chow, Lin, American Journal of Gastroenterology, Vol. 95, No. 12), the authors include a discussion of whether antibiotic treatment of bacteria
PET CT Compared to MRI In the article “Whole-Body Dual-Modality PET CT and Whole Body MRI for Tumor Staging in Oncology” (Antoch et al., Journal of the American Medical Association, Vol. 290, No. 24), the authors cite the importance of accurately identifying the stage of a tumor. Accurate
Treating Athlete’s Foot Repeat Exercise 13 after changing the frequency of 22 to 66.
Treating Athlete’s Foot As in the example of this section, assume that subjects are inflicted with athlete’s foot on each of their feet. Also assume that for each subject, one foot is treated with a fungicide solution while the other foot is given a placebo. The results are given in the
Conclusion Based on the preceding results, what do you conclude? How does the conclusion make sense in terms of the original sample results?
Critical value Using a 0.01 significance level, find the critical value.
Test statistic Using the appropriate frequencies, find the value of the test statistic.
Discordant Pairs Which of the following pairs of before/after results are discordant?a. smoke smokeb. smoke don’t smokec. don’t smoke smoked. don’t smoke don’t smoke
Why not t test? Section 9-4 presented procedures for dealing with data consisting of matched pairs. Why can’t we use the procedures of Section 9-4 for the analysis of the results summarized in the table?
Treatment Ineffectiveness How many subjects appear to be unaffected by the treatment one way or the other?
Treatment Effectiveness How many subjects changed their smoking status after the treatment?
Discordant Pairs Why does McNemar’s test involve only discordant pairs of data while ignoring the other data?5. Sample Size How many subjects are included in the experiment?
Discordant Pairs What are discordant pairs of results?
McNemar’s Test Can McNemar’s test be used on two-way tables with more than two rows or more than two columns? Why or why not?
McNemar’s Test When conducting hypothesis tests with 2 3 2 tables, what circumstances indicate that McNemar’s test is suitable while the methods of Section 11-3 are not?
Equivalent Tests Assume that a contingency table has two rows and two columns with frequencies of a and b in the first row and frequencies of c and d in the second row.a. Verify that the test statistic can be expressed asb. Let and let Show that the test statistic where and is such that z2 5 x2
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 below. At the 0.01 significance level, test the claim that the cooperation of the subject (response or refusal) is independent of the age category.
Injuries and Motorcycle Helmet Color An example in this section involved data from a case-control study involving injuries and the color of helmets of motorcycle riders.Use the additional data included in the table below and test the claim that injuries are independent of helmet color. Do these
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 Police Cashiers Taxi Drivers Guards Homicide 82 107 70 59
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?
Flipping and Spinning Pennies When flipping a penny or spinning a penny, is the probability of getting heads the same? Use the data in the table below with a 0.05 significance level to test the claim that the proportion of heads is the same with flipping as with spinning. (The data are from
Which Treatment Is Better? A randomized controlled trial was designed to compare the effectiveness of splinting against surgery in the treatment of carpal tunnel syndrome.Results are given in the table below (based on data from “Splinting vs.Surgery in the Treatment of Carpal Tunnel Syndrome,”
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
Can Dogs Detect Cancer? An experiment was conducted to test the ability of dogs to detect bladder cancer. Dogs were trained with urine samples from bladder cancer patients and people in a control group who did not have bladder cancer. Results are given in the table below (based on data from the New
Birth Weight and Graduation The data in the table below are based on data from a Time magazine article. Use a 0.05 significance level to test the claim that whether a subject had low birth weight or normal birth weight is independent of whether the subject graduates from high school by age 19. Do
Left-Handedness and Gender The table below is based on data from a Scripps Survey Research Center poll. Use a 0.05 significance level to test the claim that gender and left-handedness are independent.Left-handed Not Left-handed Male 83 17 Female 184 16
Pedestrian Fatalities A study was conducted of the association between intoxication and pedestrian deaths, with the results shown in the accompanying table (based on data from the National Highway Traffic Safety Administration). Use a 0.05 significance level to test the claim that pedestrian
Is the Vaccine Effective? In a USA Today article about an experimental 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 a placebo.” The
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
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
Causation Assume that we reject the null hypothesis of independence between the row variable of whether a subject smokes and the column variable of whether the subject can pass a standard test of physical endurance. Can we conclude that smoking causes people to fail the test? Why or why not?
Contingency What does the word “contingency” mean in the context of this section?
2. Right-Tailed Test Why are the hypothesis tests described in this section always righttailed?
Chi-Square Test Statistic Use your own words to describe what the chi-square test statistic measures when used in this section.
29. Testing Goodness-of-Fit with a Binomial Distribution An observed frequency distribution is as follows:pˆ 5 ƒ1> sƒ1 1 ƒ2d, z 5 spˆ 2 pd>2pq>n sƒ1 1 ƒ2d>2.Leading digit 1 2 3 4 5 6 7 8 9 Frequency 72 23 26 20 21 18 8 8 4 Number of successes 0 1 2 3 Frequency 89 133 52 26a. Assuming a
28. 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 8-3). Assume that a particular multinomial experiment has only two possible outcomes, A and B, with
27. 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
26. 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 10 after changing the frequency for the right rear tire
25. Author’s Check Amounts and Benford’s Law Figure 11-6(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
24. 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 5-5 we presented an example and included a table of actual frequencies of hits and the frequencies
23. Participation in Clinical Trials by Race A study was conducted to investigate racial disparity in clinical trials of cancer. Among the randomly selected participants, 644 were white, 23 were Hispanic, 69 were black, 14 were Asian Pacific Islander, and 2 were American Indian Alaskan Native. The
22. 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
21. M&M Candies Mars, Inc. claims that its M&M plain candies are distributed with the following color percentages: 16% green, 20% orange, 14% yellow, 24% blue, 13%red, and 13% brown. Refer to Data Set 13 in Appendix B and use the sample data to test the claim that the color distribution is as
20. Genetics Experiment Based on the genotypes of parents, offspring are expected to have genotypes distributed in such a way that 25% have genotypes denoted by AA, 50% have genotypes denoted by Aa, and 25% have genotypes denoted by aa. When 145 offspring are obtained, it is found that 20 of them
19. World Series Games The USA Today headline of “Seven-game series defy odds” referred to a claim that seven-game World Series contests occur more often than expected by chance. Listed below are the numbers of games of World Series contests(omitting two that lasted eight games) along with the
18. Eye Color Experiment A researcher has developed a theoretical model for predicting eye color. After examining a random sample of parents, she predicts the eye color of the first child. The table below lists the eye colors of offspring. Based on her theory, she predicted that 87% of the
17. June Bride A wedding caterer randomly selects clients from the past few years and records the months in which the wedding receptions were held. The results are listed below (based on data from The Amazing Almanac). Use a 0.05 significance level to test the claim that weddings are held in the
16. Oscar-Winning Actors The author collected data consisting of the month of birth of actors who won Oscars. Use a 0.05 significance level to test the claim that Oscarwinning actors are born in the different months with the same frequency. Compare the results to those found in Exercise 15.
15. Oscar-Winning Actresses The author collected data consisting of the month of birth of actresses who won Oscars. Use a 0.05 significance level to test the claim that Oscar-winning actresses are born in the different months with the same frequency. Is there any reason why Oscar-winning actresses
14. 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
13. Motorcycle Deaths Randomly selected deaths of motorcycle riders are summarized in the table below (based on data from the Insurance Institute for Highway Safety).Use a 0.05 significance level to test the claim that such fatalities occur with equal frequency in the different months. How might
12. Births Randomly selected birth records were obtained and results are listed in the table below (based on data from the National Vital Statistics Report, Vol. 49, No. 1).Use a 0.05 significance level to test the reasonable claim that births occur with equal frequency on the different days of the
11. Deaths from Car Crashes Randomly selected deaths from car crashes were obtained, and the results are included in the table below (based on data from the Insurance Institute for Highway Safety). Use a 0.05 significance level to test the claim that car crash fatalities occur with equal frequency
10. 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
9. 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
8. 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 10 different categories of outcome,
7. 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
6. Testing for Categories with Different Proportions Here are the observed frequencies from four categories: 5, 10, 10, 20. Assume that we want to use a 0.05 significance level to test the claim that the four categories have proportions of 0.20, 0.25, 0.25, and 0.30, respectively.a. What is the
5. Testing for Equally Likely Categories Here are the observed frequencies from three categories: 5, 5, 20. Assume that we want to use a 0.05 significance level to test the claim that the three categories are all equally likely.a. What is the null hypothesis?b. What is the expected frequency for
4. Weights of Students A researcher collects weights of 20 male students randomly selected from each of four different classes, then he finds the total of those weights and summarizes them in the table below (based on data from the National Health>Using Technology STATDISK First enter the observed
3. Observed Expected Frequencies What is an observed frequency? What is an expected frequency?
2. Right-Tailed Test Why is the hypothesis test for goodness-of-fit always a right-tailed test?
1. Goodness-of-Fit What does it mean when we say that we test for “goodness-of-fit”?
5. Which of the preceding results is best for determining whether the drug treatment is effective in reducing pain? Which of the preceding results is least effective in determining whether the drug treatment is effective in reducing pain? Based on the preceding results, does the drug appear to be
4. The methods of Section 9-4 can be used to test a claim about matched data. Identify the specific claim that the treatment is effective, then use the methods of Section 9-4 to test that claim.
3. The methods of Section 9-3 can be used to test the claim that two populations have the same mean. Identify the specific claim that the treatment is effective, then use the methods of Section 9-3 to test that claim. The methods of Section 9-3 are based on the requirement that the samples are
2. Use the given data to find the equation of the regression line. Let the response (y)variable be the pain intensity after the treatment. What would be the equation of the regression line for a treatment having absolutely no effect?
1. Use the given data to construct a scatterplot, then use the methods of Section 10-2 to test for a linear correlation between the pain intensity before the treatment and after the treatment. If there is a significant linear correlation, does it follow that the drug treatment is effective?
8. Out-of-class activity 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 there is a significant linear correlation. Also identify the regression
7. In-class activity 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 investigate correlation and regression. State your conclusions and try to
6. In-class activity Collect data from each student consisting of the number of credit cards and the number of keys that the student has in his or her possession. Is there a correlation? If so, what is it? Try to identify at t 5 !d>487.68.d s1 1 !5d>2 < 1.6. t 5 !d>192 least one reasonable
5. In-class activity Divide into groups of 8 to 12 people.For each group member, record the pulse rate by counting the number of heart beats in 1 min. Also record height. Is there a relationship between pulse rate and height? If so, what is it?
4. In-class activity 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 catch the ruler when it is released. Record the distance that the ruler falls
3. In-class activity Divide into groups of 8 to 12 people. For each group member, use a string and ruler to measure head circumference and forearm length. Is there a relationship between these two variables? If so, what is it?
2. In-class activity Divide into groups of 8 to 12 people.For each group member, measure height and arm span.For the arm span, the subject should stand with arms extended, like the wings on an airplane. It’s easy to mark the height and arm span on a chalkboard, then measure the distances there.
1. In-class activity 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 correlation between height and navel height? If so, find the regression equation with

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