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Seeing Through Statistics 2nd Edition Jessica M. Utts - Solutions
10. Suppose a meta-analysis on the risks of drinking coffee included 100,000 participants of all ages across 80 studies. One of the conclusions was that a confidence interval for the relative risk of heart attack for women over 70 who drank coffee, compared with those who didn’t, was 0.90 to
9. Give two reasons why researchers might not want to include all possible studies in a meta-analysis of a certain topic.
8. Would the file drawer problem be more likely to present a substantial difficulty in a research field with 50 researchers or in one with 1000 researchers? Explain.
7. In a meta-analysis, researchers can choose either to combine results across studies to produce a single confidence interval or to report separate confidence intervals for each study and compare them. Give one advantage and one disadvantage of combining the results into one confidence interval.
6. An article in the Sacramento Bee (15 April 1998, pp. A1, A12), titled “Drug reactions a top killer, research finds,” reported a study estimating that between 76,000 and 137,000 deaths a year in the United States occur due to adverse reactions to medications. Here are two quotes from the
5. Refer to Exercise 3. Pick three of the possible problems with meta-analysis listed in Section 24.4 and discuss how they might apply to the reviews in the Cochrane Database.
4. Refer to Exercise 3. Pick one of the benefits of meta-analysis listed in Section 24.3 and explain how that benefit applies to the reviews in the Cochrane Database.
3. According to a report in New Scientist (Vine, 21 January 1995), the UK Cochrane Centre in Oxford is launching the Cochrane Database of Systematic Reviews, which will “focus on a number of diseases, drawing conclusions about which treatments work and which do not from all the available
2. Explain why the person deciding which studies to include in a meta-analysis should be told how each study was conducted but not the results of the study.
1. Explain why the vote-counting method is not a good way to summarize the results in a research area.
2. Find two journal articles, one that reports on a statistically significant result and one that reports on a nonsignificant result. Discuss the role of the sample size in the determination of statistical significance, or lack thereof, in each case. Discuss whether you think the researchers would
1. Find a newspaper article that you think presents the results of a hypothesis test in a misleading way. Explain why you think it is misleading. Rewrite the appropriate part of the article in a way that you consider to be not misleading. If necessary, find the original journal report of the study
17. Would it be easier to reject hypotheses about populations that had a lot of natural variability in the measurements or a little variability in the measurements?Explain.
16. Now that you understand the reasoning behind making inferences about populations based on samples (confidence intervals and hypothesis tests), explain why these methods require the use of random, or at least representative, samples instead of convenience samples.
15. Explain why it is not wise to accept a null hypothesis.
13. In the study by Lee Salk, reported in Case Study 1.1, he found that infants who listened to the sound of a heartbeat in the first few days of life gained more weight than those who did not. In searching for potential explanations, Salk wrote the following. Discuss Salk’s conclusion and the
12. The authors of the report in Case Study 23.1, comparing the psychological health of UFO observers and nonobservers, presented a table in which they compared the four groups of volunteers on each of 20 psychological measures.For each of the measures, the null hypothesis was that there were no
11. When the Steering Committee of the Physicians’ Health Study Research Group(1988) reported the results of the effect of aspirin on heart attacks, committee members also reported the results of the same aspirin consumption, for the same sample, on strokes. There were 80 strokes in the aspirin
10. Refer to Case Study 22.1, concerning the ganzfeld procedure for testing ESP. In earlier studies using the ganzfeld procedure, the results were mixed in terms of whether they were statistically significant. In other words, some of the experiments were statistically significant and others were
9. We have learned that the probability of making a type 1 error when the null hypothesis is true is usually set at 5%. The probability of making a type 2 error when the alternative hypothesis is true is harder to find. Do you think that probability depends on the size of the sample? Explain your
8. The top story in USA Today on December 2, 1993, reported that “two research teams, one at Harvard and one in Germany, found that the risk of a heart attack during heavy physical exertion . . . was two to six times greater than during less strenuous activity or inactivity” (Snider, 2 December
7. Explain why it is important to learn what sample size was used in a study for which “no difference” was found.
6. In reporting the results of a study to compare two population means, explain why researchers should report each of the following:a. A confidence interval for the difference in the meansb. A p-value for the results of the test, as well as whether it was one- or two-sidedc. The sample sizes usedd.
5. New Scientist (Mestel, 12 November 1994) reported a study in which psychiatrist Donald Black used the drug fluvoxamine to treat compulsive shoppers:In Black’s study, patients take the drug for eight weeks, and the effect on their shopping urges is monitored. Then the patients are taken off the
4. In Example 4 of Chapter 22, we revisited data from Case Study 6.3, regarding testing to see if there was a relationship between gender and driving after drinking.We found that we could not rule out chance as an explanation for the sample data; the chi-squared statistic was 1.637 and the p-value
3. An article in Time magazine (Gorman, 6 February 1995) reported that an advisory panel recommended that the Food and Drug Administration (FDA) allow an experimental AIDS vaccine to go forward for testing on 5000 volunteers.The vaccine was developed by Jonas Salk, who developed the first effective
2. Refer to Case Study 23.2, in which a report stated that Internet use was associated with a statistically significant increase in depression.a. Would it have been more appropriate to use one-sided or two-sided hypothesis tests for that research? Explain.b. Explain what would have constituted a
1. An advertisement for Claritin, a drug for seasonal nasal allergies, made this claim: “Clear relief without drowsiness. In studies, the incidence of drowsiness was similar to placebo” (Time, 6 February 1995, p. 43). The advertisement also reported that 8% of the 1926 Claritin takers and 6% of
2. Conduct a test for extrasensory perception. You can either create target pictures or use a deck of cards and ask people to guess suits or colors. Whatever you use, be sure to randomize properly. For example, with a deck of cards you should always replace the previous target and shuffle very
1. Find three separate journal articles that report the results of hypothesis tests. For each one, do or answer the following:a. State the null and alternative hypotheses.b. Based on the p-value reported, what conclusion would you make?c. What would a type 1 and a type 2 error be for the hypotheses
18. In Example 2 in this chapter, we tested to see whether dieters and exercisers had different average fat loss. We concluded that they did because the difference for the samples under consideration was 1.8 kg, with a measure of uncertainty of 0.83 kg and a standardized score of 2.17. Fat loss was
17. On January 30, 1995, Time magazine reported the results of a poll of adult Americans, in which they were asked, “Have you ever driven a car when you probably had too much alcohol to drive safely?” The exact results were not given, but from the information provided we can guess at what they
16. In Chapter 12, we computed the chi-squared statistic for the data shown in Table 22.2 to be 4.82.a. Specify the hypotheses that were being examined in this study.b. Verify that the p-value accompanying this test is about 0.03.c. Suppose a friend were to try to explain to you that a p-value of
15. In Case Study 12.1, we explored data from an extrasensory perception study that used both static photos and videos as target material. We found that there was a statistically significant relationship between type of target and whether the trial was a success. The chi-squared statistic was
14. For the data in Chapter 12, Example 4, we found that the risk of developing breast cancer was 1.33 times greater for women who had their first child at age 25 or older, compared with women who had their first child before age 25.a. Specify the null and alternative hypotheses for this study.b.
13. Professors and other researchers use scholarly journals to publish the results of their research. However, only a small minority of the submitted papers are accepted for publication by the most prestigious journals. In many academic fields, there is a debate as to whether submitted papers
12. In Example 2 in this chapter, we tested whether the average fat lost from 1 year of dieting versus 1 year of exercise was equivalent. The study also measured lean body weight (muscle) lost or gained. The average for the 47 men who exercised was a gain of 0.1 kg, which can be thought of as a
11. Refer to Exercise 10. Here is another of the results reported by Siegel: “For subjects without a pet, having an above-average number of stressful life events resulted in about two more doctor contacts during the study year (10.37 vs.8.38, p < .005). In contrast, the number of stressful life
10. Siegel (1993) reported a study in which she measured the effect of pet ownership on the use of medical care by the elderly. She interviewed 938 elderly adults. One of her results was reported as: “After demographics and health status were controlled for, subjects with pets had fewer total
9. On July 1, 1994, The Press of Atlantic City, NJ, had a headline reading, “Study:Female hormone makes mind keener” (p. A2). Here is part of the report:Halbreich said he tested 36 post-menopausal women before and after they started the estrogen therapy. He gave each one a battery of tests that
8. Specify what a type 1 and a type 2 error would be for Example 4, in which we tested whether there was a relationship between gender and driving after drinking alcohol. Remember that the Supreme Court used the data to determine whether a law was justified. The law differentiated between the ages
7. Suppose you wanted to see whether a training program helped raise students’scores on a standardized test. You administer the test to a random sample of students, give them the training program, then readminister the test. For each student, you record the increase (or decrease) in the test
6. In Example 3, we showed that the Excel command NORMSDIST(z) gives the area below the standardized score z. Use Excel or another computer or calculator function to find the p-value for each of the following examples and case studies, taking into account whether the test is one-sided or
5. Suppose you were given a hypothesized population mean, a sample mean, a sample standard deviation, and a sample size for a study involving a random sample from one population. What would you use as the test statistic?
4. Suppose a two-sided test for a difference in two means resulted in a p-value of 0.08.a. Using the usual criterion for hypothesis testing, would we conclude that there was a difference in the population means? Explain.b. Suppose the test had been constructed as a one-sided test instead, and the
3. Suppose a one-sided test for a proportion resulted in a p-value of 0.03. What would the p-value be if the test were two-sided instead?
2. Refer to Exercise 1. Is the test described there a one-sided or a two-sided test?
1. In Exercise 12 in Chapter 19, we learned that in a survey of 507 adult American Catholics, 59% answered yes to the question, “Do you favor allowing women to be priests?”a. Set up the null and alternative hypotheses for deciding whether a majority of American Catholics favor allowing women to
2. Find two newspaper articles reporting on the results of studies with the following characteristics. First, find one that reports on a study that failed to find a relationship. Next, find one that reports on a study that did find a relationship.For each study, state what hypotheses you think the
1. Construct a situation for which you can test null and alternative hypotheses for a population proportion. For example, you could see whether you can flip a coin in a manner so as to bias it in favor of heads. Or you could conduct an ESP test in which you ask someone to guess the suits in a deck
19. In Case Study 1.1, Lee Salk did an experiment to see if hearing the sound of a human heartbeat would help infants gain weight during the first few days of life. By comparing weight gains for two sample groups of infants, he concluded that it did. One group listened to a heartbeat and the other
18. In Case Study 1.2 and in Chapter 12, we examined a study showing that there appears to be a relationship between taking aspirin and incidence of heart attack. The null hypothesis in that study would be that there is no relationship between the two variables, and the alternative would be that
17. Many researchers decide to reject the null hypothesis as long as the p-value is 0.05 or less. In a testing situation for which a type 2 error is much more serious than a type 1 error, should researchers require a higher or a lower p-value in order to reject the null hypothesis? Explain your
16. Consider medical tests in which the null hypothesis is that the patient does not have the disease and the alternative hypothesis is that he or she does.a. Give an example of a medical situation in which a type 1 error would be more serious.b. Give an example of a medical situation in which a
15. An article in the Los Angeles Times (24 December 1994, p. A16) announced that a new test for detecting HIV had been approved by the Food and Drug Administration (FDA). The test requires the person to send a saliva sample to a lab. The article described the accuracy of the test as follows:The
14. Suppose that a study is designed to choose between the hypotheses:Null hypothesis: Population proportion is 0.25.Alternative hypothesis: Population proportion is higher than 0.25.On the basis of a sample of size 500, the sample proportion is 0.29. The standard deviation for the potential sample
13. A report in the Davis (CA) Enterprise (6 April 1994, p. A-11) was headlined,“Highly educated people are less likely to develop Alzheimer’s disease, a new study suggests.”a. State the null and alternative hypotheses the researchers would have used in this study.b. What do you think the
12. In previous chapters, we learned that researchers have discovered a link between vertex baldness and heart attacks in men.a. State the null hypothesis and the alternative hypothesis used to investigate whether there is such a relationship.b. Discuss what would constitute a type 1 error in this
11. Given the convention of declaring that a result is statistically significant if the p-value is 0.05 or less, what decision would be made concerning the null and alternative hypotheses in each of the following cases? Be explicit about the wording of the decision.a. p-value = 0.35b. p-value = 0.04
10. Specify what a type 1 and a type 2 error would be for the ganzfeld studies reported in Case Study 21.1.
9. Compute a 95% confidence interval for the probability of a successful session in the ganzfeld studies reported in Case Study 21.1.
8. Explain why we can specify the probability of making a type 1 error, given that the null hypothesis is true, but we cannot specify the probability of making a type 2 error, given that the alternative hypothesis is true.
7. For each of the situations in Exercise 6, explain the two errors that could be made and what the consequences would be.
6. State the null and alternative hypotheses for each of the following potential research questions:a. Does working 5 hours a day or more at a computer contribute to deteriorating eyesight?b. Does placing babies in an incubator during infancy lead to claustrophobia in adult life?c. Does placing
5. An article in Science News reported on a study to compare treatments for reducing cocaine use. Part of the results are short-term psychotherapy that offers cocaine abusers practical strategies for maintaining abstinence sparks a marked drop in their overall cocaine use. . . .In contrast, brief
4. The journal article reporting the experiment described in Case Study 20.1 (see Thys-Jacobs et al., 1998, in Chapter 20) compared the placebo and calciumtreated groups for a number of PMS symptoms, both before the treatment began(baseline) and in the third cycle. A p-value was given for each
3. Refer to Case Study 20.1, in which women were randomly assigned to receive either a placebo or calcium, and severity of premenstrual syndrome (PMS)symptoms was measured.a. What are the null and alternative hypotheses tested in this experiment?b. The researchers concluded that calcium helped
2. Refer to Exercise 1. If we had conducted the hypothesis test, the resulting p-value would be 0.01. Explain what the p-value represents for this example.
1. When we revisited Case Study 6.4 in Chapter 20, we learned that a 95% confidence interval for the difference in years of education for mothers who did not smoke compared with those who did extended from 0.15 to 1.19 years, with higher education for those who did not smoke. Suppose we had used
3. Collect data on a measurement variable for which the difference in the means for two conditions or groups is of interest to you. Collect at least 30 observations for each condition or group. Using the data, compute a 95% confidence interval for the difference in the means of the populations from
2. Collect data on a measurement variable for which the mean is of interest to you.Collect at least 30 observations. Using the data, compute a 95% confidence interval for the mean of the population from which you drew your observations.Explain how you collected your sample and note whether your
1. Find a journal article that reports at least one 95% confidence interval. Explain what the study was trying to accomplish. Give the results as reported in the article in terms of 95% confidence intervals. Interpret the results. Discuss whether you think the article accomplished its intended
19. Refer to Case Study 20.1 and the material in Part 1 of this book.a. In their original report, Thys-Jacobs and colleagues (1998) noted that the study was “double-blind.” Explain what that means in the context of this example.b. Explain why it is possible to conclude that, based on this
18. Refer to Exercise 17. Suppose that from that same data set, we want to compute the average difference between the heights of adult British men and adult British women—not the average difference within married couples.a. Which of the two methods in Exercise 17 would be appropriate for this
17. Using the data presented by Hand and colleagues (1994) and discussed in previous chapters, we would like to estimate the average age difference between husbands and wives in Britain. Recall that the data consisted of a random sample of 200 couples. Following are two methods that were used to
16. A story in Newsweek (14 November 1994, pp. 52–54) reported the results of a poll asking 756 American adults the question, “Do you think Clarence Thomas sexually harassed Anita Hill, as she charged three years ago?” The results of a similar poll 3 years earlier were also reported. The
15. Parts a–d below provide additional results for Case Study 20.1. For each of the parts, compute a 95% confidence interval for the difference in mean symptom scores between the placebo and calcium-treated conditions for the symptom listed. In each case, the results given are mean ± standard
14. Refer to Case Study 20.1, illustrating the role of calcium in reducing the symptoms of PMS. Using the caution given at the end of the section, explain why we cannot use the method presented in Section 20.2 to compare baseline symptom scores with third cycle symptom scores for the
13. In a report titled, “Secondhand Smoke: Is It a Hazard?” (Consumer Reports, January 1995, pp. 27–33), 26 studies linking secondhand smoke and lung cancer were summarized by noting, “Those studies estimated that people breathing secondhand smoke were 8 to 150 percent more likely to get
12. In revisiting Case Study 5.3, we quoted the original journal article as reporting that “for any vertex baldness (i.e., mild, moderate, and severe combined), the age-adjusted RR was 1.4 (95% CI, 1.2 to 1.9)” (Lesko et al., 1993, p. 1000).Interpret this result.
11. In a study comparing age of death for left- and right-handed baseball players, Coren and Halpern (1991, p. 93) provided the following information: “Mean age of death for strong right-handers was 64.64 years (SD = 15.5, n = 1472);mean age of death for strong left-handers [was] 63.97 years (SD
10. In Case Study 6.4, which examined maternal smoking and child’s IQ, one of the results reported in the journal article was the average number of days the infant spent in the neonatal intensive care unit. The results showed an average of 0.35 day for infants of nonsmokers and an average of 0.58
9. In revisiting Case Study 6.2, we computed a confidence interval for the difference in mean DHEA-S levels for 45- to 49-year-old women meditators and nonmeditators and concluded that there probably was a real difference in the population means because most of the interval was above zero. Now we
8. In Chapter 19, we learned that to compute a 90% confidence interval, we add and subtract 1.645 rather than 2 times the measure of uncertainty. In this chapter, we revisited Case Study 6.2 and found that a 95% confidence interval for the difference in mean DHEA-S levels for 45- to 49-year-old
7. Suppose you were given a 95% confidence interval for the relative risk of disease under two different conditions. What could you conclude about the risk of disease under the two conditions if:a. The confidence interval did not cover 1.0b. The confidence interval did cover 1.0
6. Suppose you were given a 95% confidence interval for the difference in two population means. What could you conclude about the population means if:a. The confidence interval did not cover zerob. The confidence interval did cover zero
5. Suppose a university wants to know the average income of its students who work, and all students supply that information when they register. Would the university need to use the methods in this chapter to compute a confidence interval for the population mean income? Explain. (Hint: What is the
4. What is the probability that a 95% confidence interval will not cover the true population value?
3. The Baltimore Sun (Haney, 21 February 1995) reported on a study by Dr. Sara Harkness, in which she compared the sleep patterns of 6-month-old infants in the United States and the Netherlands. She found that the 36 U.S. infants slept an average of just under 13 hours out of every 24, whereas the
2. Explain the difference between a population mean and a sample mean using one of the studies discussed in the chapter as an example.
1. In Chapter 19, we saw that to construct a confidence interval for a population proportion it was enough to know the sample proportion and the sample size. Is the same true for constructing a confidence interval for a population mean? That is, is it enough to know the sample mean and sample size?
3. Choose a categorical variable for which you would like to estimate the true proportion that fall into a certain category. Conduct an experiment or a survey that allows you to find a 95% confidence interval for the proportion of interest.Explain exactly what you did, how you computed your
2. Collect data and construct a confidence interval for a proportion for which you already know the answer. Use a sample of at least 100. You can select the situation for which you would like to do this. For example, you could flip a coin 100 times and construct a confidence interval for the
1. You are going to use the methods discussed in this chapter to estimate the proportion of all cars in your area that are red. Stand on a busy street and count cars as they pass by. Count 100 cars and keep track of how many are red.a. Using your data, compute a 95% confidence interval for the
17. Refer to the formula for a confidence interval in the For Those Who Like Formulas section.a. Write the formula for a 90% confidence interval for a proportion.b. Refer to Example 6. Construct a 90% confidence interval for the proportion of smokers who would quit after 8 weeks using a nicotine
16. In Example 5 in this chapter, we found a 95% confidence interval for the proportion of successes likely in a certain kind of ESP test. Construct a 99.7% confidence interval for that example. Explain why a skeptic of ESP would prefer to report the 99.7% confidence interval.
15. A study first reported in the Journal of the American Medical Association(7 December 1994) received widespread attention as the first wide-scale study of the use of alcohol on American college campuses and was the subject of an article in Time magazine (19 December 1994, p. 16). The researchers
14. Refer to the article discussed in Exercise 13. The article continued by reporting that of those who do believe the world will come to an end, 33% believe it will happen within either a few years or a few decades. Respondents were only asked that question if they answered yes to the question
13. U.S. News and World Report (19 December 1994, pp. 62–71) reported on a survey of 1000 American adults, conducted by telephone on December 2–4, 1994, designed to measure beliefs about apocalyptic predictions. They reported that the margin of error was “±3 percentage points.”a. Verify
12. In a special double issue of Time magazine, the cover story featured Pope John Paul II as “man of the year” (26 December 1994–2 January 1995, pp. 74–76).As part of the story, Time reported on the results of a survey of 507 adult American Catholics, taken by telephone on December 7–8.
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