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statistics principles and methods
Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions
=+a. Estimate the difference between the proportion of cardiologists and the proportion of internists who did not know that carbohydrate was the diet component most likely to raise triglycerides using a 95% confidence interval.
=+of nutrition that was mailed to 6000 physicians selected at random from a list of physicians licensed in the United States. Sixteen percent of those who received the questionnaire completed and returned it. The authors report that 26 of 120 cardiologists and 222 of 419 internists did not know
=+11.51 The authors of the paper “Inadequate Physician Knowledge of the Effects of Diet on Blood Lipids and Lipoproteins” (Nutrition Journal [2003]: 19–26) summarize the responses to a questionnaire on basic knowledge
=+there sufficient evidence to conclude that the proportion of parents who regard science and mathematics as crucial is different than the corresponding proportion for students in grades 6–12? Test the relevant hypotheses using a significance level of .05.
=+and higher-level math. The two samples—parents and students—were selected independently of one another. Is
=+that 50% of students thought that understanding science and having strong math skills are essential for them to succeed in life after school, whereas 62% of the parents thought it was crucial for today’s students to learn science
=+administered by injection and flu vaccine administered as a nasal spray. Each of the 8000 children under the age of 5 that participated in the study received both a nasal spray
=+and an injection, but only one was the real vaccine and the other was salt water. At the end of the flu season, it was determined that 3.9% of the 4000 children receiving the
=+11.54 The following quote is from the article “Canadians Are Healthier Than We Are” (Associated Press, May 31, 2006): “The Americans also reported more heart disease and major depression, but those differences were too small
=+43 percent versus 25 percent.” For purposes of this exercise, suppose that these percentages were based on random samples of size 200 from each of the two groups of interest (college graduates and those without a high school degree). Is there convincing evidence that the proportion
=+11.53 “Smartest People Often Dumbest About Sunburns”is the headline of an article that appeared in the San Luis Obispo Tribune (July 19, 2006). The article states that“those with a college degree reported a higher incidence of sunburn that those without a high school degree—
=+confidence interval, would you conclude that the proportion of children who get the flu is different for the two vaccination methods?
=+who get sick with the flu after being vaccinated with the nasal spray using a 99% confidence interval. Based on the
=+b. Use the given data to estimate the difference in the proportion of children who get sick with the flu after being vaccinated with an injection and the proportion of children
=+a. Why would the researchers give every child both a nasal spray and an injection?
=+real vaccine by nasal spray got sick with the flu and 8.6%of the 4000 receiving the real vaccine by injection got sick with the flu.
=+11.50 Public Agenda conducted a survey of 1379 parents and 1342 students in grades 6–12 regarding the importance of science and mathematics in the school curriculum(Associated Press, February 15, 2006). It was reported
=+group. Of the 529 individuals in the regular chip group, 93 experienced gastrointestinal symptoms, whereas 90 of the 563 individuals in the olestra chip group experienced symptoms. Carry out a hypothesis test at the 5% significance level to decide whether the proportion of individuals who
=+c. Based on the intervals from Parts (a) and (b), do you think the mean change in blood lactate level is the same for men as it is for women? Explain.11.44 proces a telep access random and 60
=+b. Estimate the mean change for female players using a 90% confidence interval.
=+a. Estimate the mean change in blood lactate level for male racquetball players using a 90% confidence interval.
=+were measured before and after playing three games of racquetball, as shown in the accompanying table.Men Women Player Before After Player Before After 1 13 18 1 11 21 2 20 37 2 16 26 3 17 40 3 13 19 4 13 35 4 18 21 5 13 30 5 14 14 6 16 20 6 11 31 7 15 33 7 13 20 8 16 19
=+11.43 ● The effect of exercise on the amount of lactic acid in the blood was examined in the article “A Descriptive Analysis of Elite-Level Racquetball” (Research Quarterly for Exercise and Sport [1991]: 109–114). Eight men and seven women who were attending a weeklong training camp
=+1.51. Construct and interpret a 95% confidence interval for the mean difference.
=+b. The mean of the differences was 2.83 (indicating girls intended, on average, to take fewer classes than they thought boys should take), and the standard deviation was
=+a. Explain why these data are paired.
=+those who registered by phone, 57 reported that they were satisfied with the registration process. Of those who registered online, 50 reported that they were satisfied. Based on these data, is it reasonable to conclude that the proportion who are satisfied is higher for those who register
=+11.45 Some commercial airplanes recirculate approximately 50% of the cabin air in order to increase fuel efficiency. The authors of the paper “Aircraft Cabin Air Recirculation and Symptoms of the Common Cold” (Journal of the American Medical Association [2002]: 483–486) studied 1100
=+11.49 Olestra is a fat substitute approved by the FDA for use in snack foods. To investigate reports of gastrointestinal problems associated with olestra consumption, an experiment was carried out to compare olestra potato chips with regular potato chips (“Gastrointestinal Symptoms Following
=+evidence that the proportion of females that owned an MP3 player in 2006 is smaller than the corresponding proportion of males? Carry out a test using a significance level of .01.
=+11.48 The article referenced in the previous exercise also reported that 24% of the males and 16% of the females in the 2006 sample reported owning an MP3 player. Suppose that there were the same number of males and females in the sample of 1112. Do these data provide convincing
=+of size 1112. Estimate the difference in the proportion of Americans age 12 and older who owned an MP3 player in 2006 and the corresponding proportion for 2005 using a 95% confidence interval. Is zero included in the interval?What does this tell you about the change in this proportion from 2005
=+11.47 The article “Portable MP3 Player Ownership Reaches New High” (Ipsos Insight, June 29, 2006) reported that in 2006, 20% of those in a random sample of 1112 Americans age 12 and older indicated that they owned an MP3 player. In a similar survey conducted in 2005, only 15% reported owning
=+treatment that consisted of drugs plus surgery to install the stocking. After two years, 38% of the 57 patients receiving the stocking had improved and 27% of the patients receiving the standard treatment had improved. Do these data provide convincing evidence that the proportion of patients who
=+11.46 “Doctors Praise Device That Aids Ailing Hearts”(Associated Press, November 9, 2004) is the headline of an article that describes the results of a study of the effectiveness of a fabric device that acts like a support stocking for a weak or damaged heart. In the study, 107 people who
=+assume that it is reasonable to regard these two samples as being independently selected and as representative of the two populations of interest.
=+to be statistically significant.” This statement was based on the responses of a sample of 5183 Americans and a sample of 3505 Canadians. The proportion of Canadians who reported major depression was given as .082.
=+11.64 The article “Trial Lawyers and Testosterone: BlueCollar Talent in a White-Collar World” (Journal of Applied Social Psychology [1998]: 84–94) compared trial lawyers and nontrial lawyers on the basis of mean testosterone level. Random samples of 35 male trial lawyers, 31 male
=+4. If assigned to do so by your instructor, carry out one of your experiments and analyze the resulting data. Write a brief report that describes the experimental design, includes both graphical and numerical summaries of the resulting data, and communicates the conclusions that follow from
=+3. Which of the two proposed designs would you recommend, and why?
=+2. How would you modify the design from Step 1 so that the resulting data are paired? Is the way in which randomization is incorporated into the new design different from the way it is incorporated in the design from Step 1?Explain.
=+1. Working in a group, design an experiment to investigate the given research question that would result in independent samples. Be sure to describe how you plan to measure quickness of reflexes, what extraneous variables will be directly controlled, and the role that randomization plays in
=+6. Write a paragraph for the sports section of your school newspaper describing this experiment and the conclusions that can be drawn from it
=+5. Is the conclusion in the test of Step 4 consistent with your initial prediction of the outcome of this experiment?Explain.
=+4. Carry out an appropriate hypothesis test to determine whether there is convincing evidence that the mean distance traveled is greater for a helium-filled football than for an air-filled football.
=+3. There are two samples in this data set. One consists of distances traveled for the 39 kicks of the air-filled football, and the other consists of the 39 distances for the heliumfilled football. Are these samples independent or paired?Explain.
=+11.61 When a surgeon repairs injuries, sutures (stitched knots) are used to hold together and stabilize the injured area. If these knots elongate and loosen through use, the injury may not heal properly because the tissues would not be optimally positioned. Researchers at the University of
=+knots with two types of suture material, Maxon and Ticron.Suppose that 112 tissue specimens were available and that for each specimen the type of knot and suture material were randomly assigned. The investigators tested the knots to see how much the loops elongated; the elongations (in mm)were
=+For the small prey, is there a significant difference between the inexperienced and experienced snakes? For the medium prey? For the large prey?
=+Mouse Mouse Mouse s s s Inexperienced 3.1 1.0 3.4 .4 1.8 .3 Experienced 2.6 .3 2.9 .6 4.7 .3 x x x xx
=+11.62 Snake experts believe that venomous snakes inject different amounts of venom when killing their prey. Researchers at the University of Wyoming tested this hypothesis to determine whether young prairie rattlesnakes use more venom to kill larger mice and less venom for smaller mice
=+c. For the Duncan loop data, is there a significant difference between the elongations of Maxon versus Ticron threads?
=+b. Is there a significant difference between the square knot and the Duncan loop for Ticron thread?
=+a. Is there a significant difference in elongation between the square knot and the Duncan loop for Maxon thread?
=+For purposes of this exercise, assume it is reasonable to regard the elongation distributions as approximately normal.
=+2. The data from this experiment can be found in the Data and Story Library at the following web site:http://lib.stat.cme.edu/DASL/Datafiles/heliumfootball.html
=+1. Do you think that helium-filled balls will tend to travel farther than air-filled balls when kicked? Before looking at the data, write a few sentences indicating what you think the outcome of this experiment was and describing the reasoning that supports your prediction.
=+sperm counts of avid mountain bikers (those who ride at least 12 hours per week) and nonbikers. Ninety percent of the avid mountain bikers studied had low sperm counts, as compared to 26% of the nonbikers. Suppose that these percentages were based on independent samples of 100 avid mountain
=+11.57 “Mountain Biking May Reduce Fertility in Men, Study Says” was the headline of an article appearing in the San Luis Obispo Tribune (December 3, 2002). This conclusion was based on an Austrian study that compared
=+identical except that 2500 of them had “white-sounding”first names, such as Brett and Emily, whereas the other 2500 had “black-sounding” names such as Tamika and Rasheed. Resumes of the first type elicited 250 responses and resumes of the second type only 167 responses. Do these data
=+11.56 The article “A ‘White’ Name Found to Help in Job Search” (Associated Press, January 15, 2003) described an experiment to investigate if it helps to have a “whitesounding” first name when looking for a job. Researchers sent 5000 resumes in response to ads that appeared in the
=+The following data are compatible with summary values given in the report:Sample Number with Group Size Lymphoma p Exposed 827 473 .572 Unexposed 130 19 .146 Estimate the difference between the proportion of exposed dogs that develop lymphoma and the proportion of unexposed dogs that develop
=+11.55 Researchers at the National Cancer Institute released the results of a study that examined the effect of weed-killing herbicides on house pets (Associated Press, September 4, 1991). Dogs, some of whom were from homes where the herbicide was used on a regular basis, were examined for the
=+b. Assuming that the researchers used a significance level of .05, could the sample proportion of Americans reporting major depression have been as large as .10? Explain why or why not.
=+a. Assuming that the researchers used a significance level of .05, could the sample proportion of Americans reporting major depression have been as large as .09? Explain why or why not.
=+a. Do these data provide convincing evidence that the proportion of Austrian avid mountain bikers with low sperm count is higher than the proportion of Austrian nonbikers?
=+b. Based on the outcome of the test in Part (a), is it reasonable to conclude that mountain biking 12 hours per week or more causes low sperm count? Explain.
=+11.58 In a study of a proposed approach for diabetes prevention, 339 people under the age of 20 who were thought to be at high risk of developing type I diabetes were assigned at random to two groups. One group received twice-daily injections of a low dose of insulin. The other group (the
=+the disease) for the approximately 700,000 soldiers sent to the Gulf between August 1990 and July 1991 was compared to the incidence rate for the approximately 1.8 million other soldiers who were not in the Gulf during this time period. Based on these data, explain why it is not appropriate to
=+11.60 In December 2001, the Department of Veterans Affairs announced that it would begin paying benefits to soldiers suffering from Lou Gehrig’s disease who had served in the Gulf War (The New York Times, December 11, 2001).This decision was based on an analysis in which the Lou Gehrig’s
=+What hypotheses do you think the researchers tested in order to reach the given conclusion? Did the researchers reject or fail to reject the null hypothesis?
=+the two treatments (Associated Press, October 17, 2002).
=+11.59 Women diagnosed with breast cancer whose tumors have not spread may be faced with a decision between two surgical treatments—mastectomy (removal of the breast)or lumpectomy (only the tumor is removed). In a longterm study of the effectiveness of these two treatments, 701 women with
=+c. Based on your interval from Part (a), write a few sentences commenting on the effectiveness of the proposed prevention treatment.
=+b. Give an interpretation of the confidence interval and the associated confidence level.
=+a. Use the given data to construct a 90% confidence interval for the difference in the proportion that develop diabetes for the control group and the insulin group.
=+confidence interval for the mean suppertime of a vampire bat whose meal consists of a frog. What assumptions must be reasonable for the one-sample t interval to be appropriate?
=+article “Foraging Behavior of the Indian False Vampire Bat” (Biotropica [1991]: 63–67). These bats consume insects and frogs. For these 12 bats, the mean time to consume a frog was min. Suppose that the standard deviation was s 5 7.7 min. Construct and interpret a 90%
=+9.73 The eating habits of 12 bats were examined in the
=+9.72 The interval from 22.33 to 1.75 captures an area of .95 under the z curve. This implies that another largesample 95% confidence interval for m has lower limit and upper limit . Would you recommend using this 95% interval over the 95% interval discussed in the text? Explain. (Hint: Look at
=+Use the data of Exercise 9.67 to obtain a 95% confidence interval for the true standard deviation of commuting distance.
=+9.71 When n is large, the statistic s is approximately unbiased for estimating s and has approximately a normal distribution. The standard deviation of this statistic when the population distribution is normal is which can be estimated by . A large-sample confidence interval for the population
=+.99). Thus, is a 99% upper confidence bound for m. Use the data of Example 9.8 to calculate the 99%upper confidence bound for the true wait time for bypass patients in Ontario.
=+sample interval in Section 9.3, we can say that when n is large, 99% of all samples have(because the area under the z curve to the left of 2.33 is
=+9.69 The confidence intervals presented in this chapter give both lower and upper bounds on plausible values for the population characteristic being estimated. In some instances, only an upper bound or only a lower bound is appropriate. Using the same reasoning that gave the large
=+who preferred the cigarette tax increase; use a 95% confidence interval.
=+9.68 In 1991, California imposed a “snack tax” (a sales tax on snack food) in an attempt to help balance the state budget. A proposed alternative tax was a 12¢-per-pack increase in the cigarette tax. In a poll of 602 randomly selected California registered voters, 445 responded that they
=+10–2 verdict in criminal cases not involving the death penalty. The Associated Press (San Luis Obispo TelegramTribune, September 13, 1995) reported that 71% supported the 10–2 verdict. Suppose that the sample size for this survey was n 5 900. Compute and interpret a 99%confidence interval
=+9.66 Recent high-profile legal cases have many people reevaluating the jury system. Many believe that juries in criminal trials should be able to convict on less than a unanimous vote. To assess support for this idea, investigators asked each individual in a random sample of Californians
=+9.65 A manufacturer of college textbooks is interested in estimating the strength of the bindings produced by a particular binding machine. Strength can be measured by recording the force required to pull the pages from the binding. If this force is measured in pounds, how many books should be
=+sample mean rating of acceptable load attained with a work-simulating test was found to be 5 9.7 kg. and the sample standard deviation was s 5 4.3 kg. Suppose that in the population of all male postal workers, the distribution of rating of acceptable load can be modeled approximately using a
=+9.63 Increases in worker injuries and disability claims have prompted renewed interest in workplace design and regulation. As one particular aspect of this, employees required to do regular lifting should not have to handle unsafe loads. The article “Anthropometric, Muscle Strength, and
=+c. The actual sample size for this survey was much larger than 500. Would a confidence interval based on the actual sample size have been narrower or wider than the one computed in Part (a)?
=+b. Compute and interpret a 95% confidence interval for the proportion of students who are not attending their first choice of college.
=+a. Using the sample size n 5 500, calculate a 99% confidence interval for the proportion of college students who are attending their first choice of college.
=+9.62 The Chronicle of Higher Education (January 13, 1993) reported that 72.1% of those responding to a national survey of college freshmen were attending the college of their first choice. Suppose that n 5 500 students responded to the survey (the actual sample size was much larger).
=+c. The National Coalition on Television Violence claims that shows on ABC are more violent than those on the other networks. Based on the confidence intervals from Parts (a) and (b), do you agree with this conclusion?Explain.
=+b. Compute 95% confidence intervals for the mean number of violent acts per prime-time hour for each of the other three networks.
=+a. Compute a 95% confidence interval for the true mean number of violent acts per prime-time hour for ABC.
=+9.61 The McClatchy News Service (San Luis Obispo Telegram-Tribune, June 13, 1991) reported on a study of violence on television during primetime hours. The following table summarizes the information reported for four networks:Mean Number of Network Violent Acts per Hour ABC 15.6 CBS 11.9 FOX
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