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statistics informed decisions using data
Elementary Statistics 10th Edition Mario F. Triola - Solutions
30. Appendix B Data Set: Discarded Plastic and Household Size Refer to Data Set 16 in Appendix B and use the weights of discarded plastic and the corresponding household sizes.
29. Appendix B Data Set: List Price and Selling Price Refer to Data Set 18 in Appendix B and use the list prices and selling prices of homes sold.
28. State Budget and Days Late New York State has become notorious for approving the state budget after the annual deadline of April 1. The amounts of the budget (in billions of dollars adjusted for inflation) and the numbers of days late are listed below with corresponding entries representing the
27. Height and Pulse Rate A medical student hypothesizes that taller people have faster pulse rates because the blood has farther to travel. Pulse rates (beats per minute) and heights (inches) are listed below for a random sample of adult women (based on data from the National Health Examination
26. Fires and Acres Burned Listed below are the numbers of fires (in thousands) and the acres that were burned (in millions) in 11 western states in each year of the last decade (based on data from USA Today). Is there a correlation? The data were listed under a headline of “Loggers seize on
25. Crickets and Temperature One classic application of correlation involves the association between the temperature and the number of times a cricket chirps in a minute.Listed below are the numbers of chirps in 1 min and the corresponding temperatures in degrees Fahrenheit (based on data from The
24. Parent Child Heights Listed below are heights (in inches) of mothers and heights (in inches) of their daughters (based on data from the National Health Examination Survey).Does there appear to be a linear correlation between mother’s heights and the heights of their daughters?Mother’s
23. Temperatures and Marathons In “The Effects of Temperature on Marathon Runner’s Performance,” by David Martin and John Buoncristiani (Chance, Vol. 12, No. 4), high temperatures and times (in minutes) were given for women who won the New York City marathon in recent years. Results are
22. Smoking and Cotinine When nicotine is absorbed by the body, cotinine is produced.A measurement of cotinine in the body is therefore a good indicator of how much a person smokes. Listed below are the reported numbers of cigarettes smoked per day and the measured amounts of nicotine (in ng mL).
21. Buying a TVAudience 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 in theaters? Apart from the budget amount, identify
20. Murders and Population Size The table below lists the numbers of murders and the population sizes (in hundreds of thousands) for large cities in America during a recent year (based on data from the New York Times). What do you conclude?Murders 258 264 402 253 111 648 288 654 256 60 590
19. Blood Pressure Measurements Fourteen different second-year medical students took blood pressure measurements of the same patient and the results are listed below (data provided by Marc Triola, MD). Is there a correlation between systolic and diastolic values? Apart from correlation, is there
18. Supermodel Heights and Weights Listed below are heights (in inches) and weights(in pounds) for supermodels Michelle Alves, Nadia Avermann, Paris Hilton, Kelly Dyer, Christy Turlington, Bridget Hall, Naomi Campbell, Valerie Mazza, and Kristy Hume. Is there a correlation between height and
17. Bear Chest Size and Weight Listed below are the chest sizes (in inches) and weights(in pounds) of randomly selected bears that were anesthetized and measured (based on data from Gary Alt and Minitab, Inc.). Because it is much more difficult to weigh a bear than to measure its chest size, the
16. Car Weight and Fuel Consumption Listed below are the weights (in pounds) and the highway fuel consumption amounts (in mi gal) of randomly selected cars (Chrysler Sebring, Ford Mustang, BMW 3-Series, Ford Crown Victoria, Honda Civic, Mazda Protégé, Hyundai Accent). Is there a linear
15. Movie Budgets and Gross Listed below are the budgets (in millions of dollars) and the gross receipts (in millions of dollars) for randomly selected movies (based on data from the Motion Picture Association of America). Does there appear to be a linear correlation between the money spent making
14. Song Audiences and Sales The table below lists the numbers of audience impressions(in hundreds of millions) listening to songs and the corresponding numbers of albums sold (in hundreds of thousands). The number of audience impressions is a count of the number of times people have heard the
13. Old Faithful Examples in this section analyzed the correlation between duration times and time intervals after eruptions of the Old Faithful geyser. Using the data given below (from Table 10-1), is there a linear correlation between height of an eruption and the time interval after the
e. Based on the preceding results, what do you conclude? Should the data from women and the data from men be considered together, or do they appear to represent two different and distinct populations that should be analyzed separately?Testing for a Linear Correlation. In Exercises 13–28,
d. Find the value of the linear correlation coefficient using all eight points. What does that value suggest about the relationship between x and y?
12. Effects of Clusters Refer to the Minitab-generated scatterplot on the top of the next page. The four points in the lower left corner are measurements from women, and the four points in the upper right corner are from men.a. Examine the pattern of the four points in the lower left corner (from
11. Effects of an Outlier Refer to the accompanying Minitab-generated scatterplot.a. Examine the pattern of all 10 points and subjectively determine whether there appears to be a correlation between x and y.b. After identifying the 10 pairs of coordinates corresponding to the 10 points, find the
8. Ages of Marathon Runners The ages and finishing times of 150 randomly selected runners who completed the New York City Marathon were recorded. ATI-83 84 Plus calculator was used to find that the value of the linear correlation coefficient is r 0.144. (Hint: For the critical values are .)a. Is
7. Stocks and Super Bowl The Dow Jones Industrial Average (DJIA) high values and the total number of points scored in the Super Bowl were recorded for 21 different years.Excel was used to find that the value of the linear correlation coefficient is r0.133.a. Is there a linear correlation between
6. Guns and Murder Rate Using data collected from the FBI and the Bureau of Alcohol, Tobacco, and Firearms, the number of registered automatic weapons and the murder rate (in murders per 100,000 people) were obtained for each of eight randomly selected states. STATDISK was used to find that the
5. Chest Sizes and Weights of Bears When eight bears were anesthetized, researchers measured the distances (in inches) around the bears’ chests and weighed the bears (in pounds). Minitab was used to find that the value of the linear correlation coefficient is r 0.993.a. Is there a linear
4. Identify Scatterplots Given below are three scatterplots generated from STATDISK.Match the scatterplots with these values of the linear correlation coefficient: r 0.857, r0.658, r 0.012.STATDISK STATDISK STATDISK Interpreting r. In Exercises 5–8, use a significance level of a 0.05.
3. Correlation and Lurking Variable What is correlation? What is a lurking variable?
2. Adverse Drug Reaction A clinical study is conducted to investigate the effectiveness of the drug Dozenol for treating insomnia. It was found that there is a correlation between the amount of Dozenol taken and the length of sleep. Based on this statistical analysis, can we conclude that Dozenol
1. SSN and Income A government researcher wants to conduct a study to determine if there is a correlation between social security numbers and income. He collects the paired data from a random sample of 100 people. Should the methods of this section be used with the linear correlation coefficient?
8. Construct a graph which would make the results understandable to typical newspaper readers.
7. In a separate Gallup poll, 1001 randomly selected adults were asked this question:“If you had to fly on an airplane tomorrow, how would you describe your feelings about flying? Would you be—very afraid, somewhat afraid, not very afraid, or not afraid at all?” Here are the responses: very
5. What important piece of information should be included, but is not included?
5. Based on the result from the confidence interval obtained in Exercise 4, complete the following statement, which is typical of the statement that would be reported in a newspaper or magazine: “Based on the Marist Institute for Public Opinion poll, the percentage of men who fear flying is 12%
4. Construct a 95% confidence interval for the percentage of men who fear flying.
3. Construct a 95% confidence interval estimate of the difference between the percentage of men and the percentage of women who fear flying. Do the confidence interval limits contain 0, and what is the significance of whether they do or do not?
2. Is there sufficient evidence to conclude that there is a significant difference between the percentage of men and the percentage of women who fear flying?
1. How many men were surveyed? How many women were surveyed? How many of the surveyed men fear flying? How many of the surveyed women fear flying?
7. 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
6. In-class activity Without using any measuring device, each student should draw a line believed to be 3 in.long. Then use rulers to measure and record the lengths of the lines drawn. Test for a difference between the mean length of lines drawn by males and the mean length of lines drawn by
5. Out-of-class activity Construct a short survey of just a few questions, including a question asking the subject to report his or her height. After the subject has completed the survey, measure the subject’s height (without shoes)using an accurate measuring system. Record the gender, reported
4. Out-of-class activity Use a watch to record the waiting times of a sample of McDonald’s customers and the waiting times of a sample of Burger King customers.Use a hypothesis test to determine whether there is a significant difference.
3. Out-of-class activity Randomly select a sample of male students and a sample of female students and ask each selected person whether they support a death penalty for people convicted of murder. Use a formal hypothesis test to determine whether there is a gender gap on this issue.Also, keep a
2. In-class activity Divide into groups according to gender, with about 10 or 12 students in each group. Each group member should record his or her pulse rate by counting the number of heartbeats in 1 minute, and the group statistics (n, , s) should be calculated. The groups should test the null
1. Out-of-class activity Are estimates influenced by anchoring numbers? Refer to the related Chapter 3 Cooperative Group Activity. In Chapter 3 we noted that, according to author John Rubin, when people must estimate a value, their estimate is often “anchored” to (or influenced by) a preceding
3. Cell Phones and Crashes: Analyzing Newspaper Report In an article from the Associated Press, it was reported that researchers “randomly selected 100 New York motorists who had been in an accident and 100 who had not. Of those in accidents, 13.7 percent owned a cellular phone, while just 10.6
c. Using all of the results combined with a 0.01 significance level, test the claim that a coin can be tossed so that heads turns up more often than can be expected by chance.Quarter: H H H H H H H H H Penny: H H T H T H H T T
b. Are the results from the quarter independent of the results from the penny, or are the sample data matched pairs? Explain.
2. Tossing Coins An illusionist claims that she has the ability to toss a coin so that it turns up heads. Listed below are results from a test of her abilities.a. Consider only the results from the tosses of a quarter. What is the probability of getting nine heads in nine tosses if the outcomes are
d. Assuming that the speeds are from normally distributed populations, test the claim that the mean speed on the northbound lanes is equal to the mean speed on the southbound lanes. Based on the result from part (c), does it appear that this hypothesis test is likely to be valid?Highway 405 North:
c. Do the northbound speeds appear to come from a normally distributed population?Explain.
b. Using all of the speeds combined, test the claim that the mean is greater than the posted speed limit of 65 mi h.
1. Highway Speeds A section of Highway 405 in Los Angeles has a speed limit of 65 mi h, and recorded speeds are listed below for randomly selected cars traveling on northbound and southbound lanes (based on data from Sigalert.com).a. Using the speeds for the northbound lanes, find the mean, median,
8. Historical Data Set In 1908, “Student” (William Gosset) published the article “The Probable Error of a Mean” (Biometrika, Vol. 6, No. 1). He included the data listed below for two different types of straw seed (regular and kiln dried) that were used on adjacent plots of land. The listed
7. Variation of Brain Volumes Use the same sample data given in Exercise 6 with a 0.05 significance level to test the claim that the populations of total brain volumes for obsessive-compulsive patients and the control group have different amounts of variation.
c. Based on the results from parts (a) and (b), does it appear that the total brain volume can be used as an indicator of obsessive-compulsive disorders?Obsessive-compulsive patients: n 10, 1390.03, s 156.84 Control group: n 10, 1268.41, s 137.97
b. Use a 0.05 significance level to test the claim that there is no difference between the mean for obsessive-compulsive patients and the mean for healthy persons. Do not assume that the two populations have equal variances.
a. Construct a 95% confidence interval for the difference between the mean brain volume of obsessive-compulsive patients and the mean brain volume of healthy persons. Do not assume that the two populations have equal variances.
6. Brain Volume and Psychiatric Disorders A study used x-ray computed tomography(CT) to collect data on brain volumes for a group of patients with obsessivecompulsive disorders and a control group of healthy persons. Sample results (in mL)are given below for total brain volumes (based on data from
d. In general, if a confidence interval estimate of the difference between two population proportions is used to test some claim about the proportions, will the conclusion based on the confidence interval always be the same as the conclusion from a standard hypothesis test?
c. Using the confidence level from part (b), construct a confidence interval estimate of the difference between the two population proportions.
b. If a confidence interval is to be used for testing the claim in part (a), what confidence level should be used?
a. Use a 0.05 significance level to test the claim of the article’s headline: “Warmer surgical patients recover better.” If these results are verified, should surgical patients be routinely warmed?
5. Warmer Surgical Patients Recover Better? An article published in USA Today stated that “in a study of 200 colorectal surgery patients, 104 were kept warm with blankets and intravenous fluids; 96 were kept cool. The results show: Only 6 of those warmed developed wound infections vs. 18 who were
4. Variation in J. K. Rowling and Leo Tolstoy Refer to the same data used in Exercise 3 and use a 0.05 significance level to test the claim that pages from Harry Potter and 508 Chapter 9 Inferences from Two Samples the Sorcerer’s Stone and War and Peace have Flesch Reading Ease scores with the
3. Comparing Readability of J. K. Rowling and Leo Tolstoy Listed below are Flesch Reading Ease scores taken from randomly selected pages in J. K. Rowling’s Harry Potter and the Sorcerer’s Stone and Leo Tolstoy’s War and Peace. (Higher Flesch Reading Ease scores indicated writing that is
2. Self-Reported and Measured Heights of Male Statistics Students Eleven 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
1. Racial Profiling Racial profiling is the controversial practice of targeting someone for suspicion of criminal behavior on the basis of race, national origin, or ethnicity. The table below includes data from randomly selected drivers stopped by police in a recent year (based on data from the
4. Independent Samples What is the difference between two samples that are independent and two samples that are not independent?Review Exercises
3. Comparing Incomes Using data from the Bureau of Labor Statistics, a researcher obtains the mean income of men and the mean income of women for each of the 50 states. She then conducts a t test of the null hypothesis that men and women in the United States have equal mean incomes. Is this
2. Simple Random Sample You have been hired to compare the mean credit debt of men in your state to the mean credit debt of women in your state. You have been as21 s22?1 FR b , s1 2 s2 2 , a s21 s22?1 FL bs1 2 >s2 2 s2 2 s1 2 Review Exercises 507 given samples that were obtained by this process:
1. Which Method? Acandidate for political office is concerned about reports of a “gender gap” claiming that he is preferred more by male voters than by women voters. You have been hired to investigate the gender gap. What methods of this chapter would you use?
24. Constructing Confidence Intervals In addition to testing claims involving and , we can also construct confidence interval estimates of the ratio using the following expression:Here FL and FR are as described in Exercise 23. Refer to the sample data given in Exercise 5 and construct a 95%
23. Finding Lower Critical F Values In this section, for hypothesis tests that were twotailed, we need to find only the upper critical value. Let’s denote that value by FR, where the subscript indicates the critical value for the right tail. The lower critical value FL (for the left tail) can be
22. Levene-Brown-Forsythe Test for Comparing Variation in Two Populations See the example in this section and, instead of using the F test, use the Levene-Brown-Forsythe test described near the end of this section. What do you conclude?
d. If c1 critical value, then conclude that . If c2 critical value, then conclude that . Otherwise, fail to reject the null hypothesis of .
c. If the sample sizes are equal (n1 n2), use a critical value of 5. If n1 n2, calculate the critical value shown below.
b. Let c1 be the count of the number of MAD values in the first sample that are greater than the largest MAD value in the other sample. Also, let c2 be the count of the number of MAD values in the second sample that are greater than the largest MAD in the other sample. (One of these counts will
21. Count Five Test for Comparing Variation in Two Populations See the example in this section and, instead of using the F test, use the following procedure for a “count five”test of equal variation. What do you conclude?a. For the first sample, find the mean absolute deviation (MAD) of each
d. What can be concluded from the preceding results?9-5 BEYOND THE BASICS
c. Do the data appear to satisfy the requirement of normally distributed populations?Instead of constructing histograms or normal quantile plots, simply examine the numbers of movies showing no tobacco or alcohol use. Are the times for tobacco use normally distributed? Are the times for alcohol use
b. Do the data appear to satisfy the requirement of independent populations? Explain.
a. Assuming that we want to use the methods of this section to test the claim that the times of tobacco use and the times of alcohol use have different standard deviations, identify the F test statistic, critical value, and conclusion. Use a 0.05 significance level.
20. Appendix B Data Set: Tobacco and Alcohol Use in Animated Children’s Movies Data Set 5 in Appendix B lists times (in seconds) that animated children’s movies show tobacco use and alcohol use.
b. Consider the prerequisite of normally distributed populations. Instead of constructing histograms or normal quantile plots, simply examine the numbers of days with xx x x x x 9-5 Comparing Variation in Two Samples 505 no rainfall. Are Wednesday rainfall amounts normally distributed? Are Sunday
a. Assuming that we want to use the methods of this section to test the claim that Wednesday and Sunday rainfall amounts have the same standard deviation, identify the F test statistic, critical value, and conclusion. Use a 0.05 significance level.
19. Appendix B Data Set: Rainfall on Weekends USA Today and other newspapers reported on a study that supposedly showed that it rains more on weekends. The study referred to areas on the East Coast near the ocean. Data Set 10 in Appendix B lists the rainfall amounts in Boston for one year.
18. Effect of Birth Weight on IQ Score When investigating a relationship between birth weight and IQ, researchers found that 258 subjects with extremely low birth weights(less than 1000 g) had Wechsler IQ scores at age 8 with a mean of 95.5 and a variance of 256.0. For 220 subjects with normal
17. 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. Sample values consisting of measures of“debilitating test anxiety”
16. Weights of Pennies and Quarters Data Set 14 in Appendix B includes weights of post-1983 pennies and post-1964 quarters. Here are the summary statistics: post-1983 pennies: n 37, 2.49910 g, s 0.01648 g; post-1964 quarters: n 40, 5.63930 g, s 0.06194. Test the claim that post-1983
15. Weights of Quarters Weights of quarters are used by vending machines as one way to detect counterfeit coins. Data Set 14 in Appendix B includes weights of pre-1964 silver quarters and post-1964 quarters. Here are the summary statistics: pre-1964: n 40, 6.19267 g, s 0.08700 g; post-1964: n
14. Ages of Faculty and Student Cars Students at the author’s college randomly selected 217 student cars and found that they had ages with a mean of 7.89 years and a standard deviation of 3.67 years. They also randomly selected 152 faculty cars and found that they had ages with a mean of 5.99
13. 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 (based on data from
12. Hypothesis Test for Effect of Marijuana Use on College Students In a study of the effects of marijuana use, light and heavy users of marijuana in college were tested for memory recall, with the results given below (based on data from “The Residual Cognitive Effects of Heavy Marijuana Use in
11. Hypothesis Test for Magnet Treatment of Pain Researchers conducted a study to determine whether magnets are effective in treating back pain, with results given below(based on data from “Bipolar Permanent Magnets for the Treatment of Chronic Lower Back Pain: A Pilot Study,” by Collacott,
10. 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 bipolar depression,
9. Weights of Diet Coke and Diet Pepsi This section included an example about a hypothesis test of the claim that weights of regular Coke and regular Pepsi have the same standard deviation. Use a 0.05 significance level to test the claim that Diet Coke and Diet Pepsi have weights with different
8. Interpreting Display for Test of Echinacea In a randomized, double-blind, placebocontrolled trial of children, echinacea was tested as a treatment for upper respiratory infections in children. “Days of fever” was one criterion used to measure effects.Among 337 children treated with
7. Interpreting Display from Weights of Regular Coke and Diet Coke This section included an example about a hypothesis test of the claim that weights of regular Coke and regular Pepsi have the same standard deviation. Use a 0.05 significance level to test the claim that regular Coke and diet Coke
6. Claim: IQ scores of statistics students vary less than IQ scores of other students.Statistics students: n 28, 118, s 10.0 Other students: n 25, 112, s 12.0
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