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descriptive statistics
Seeing Through Statistics 3rd Edition David D Busch, Jessica M Utts - Solutions
9. Compute a 95% confidence interval for the probability of a successful session in the ganzfeld studies reported in Case Study 22.1.
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 21.1 (see Thys-Jacobs et al., 1998, in Chapter 21) 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 21.1, 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 21, 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
25. Table 1 on page 200 of Original Source 18, “Birth weight and cognitive function in the British 1946 birth cohort: longitudinal population based study” (not available for the CD), provides 95% confidence intervals for the difference in mean standardized cognitive scores for midrange
24. Refer to Original Source 11, “Driving impairment due to sleepiness is exacerbated by low alcohol intake.” Table 1 on the top of page 691 presents mean blood alcohol concentrations (BAC) and standard errors of the mean (SE in Table 1) for the participants before driving. The values are given
23. Refer to Original Source 10 on the CD, “Religious attendance and cause of death over 31 years.” Table 2 in the article provides 95% confidence intervals for the relative risk of death by various causes for those who attend religious services less than weekly versus weekly. (The relative
22. Refer to Original Source 9 on the CD, “Suicide Rates in Clinical Trials of SSRIs, Other Antidepressants, and Placebo: Analysis of FDA Reports.” Table 1 in that paper (page 791) provides confidence intervals for suicide rates for patients taking three different kinds of medications. For
*21. Refer to Original Source 5 on the CD, “Distractions in Everyday Driving.” Table 14 on page 51 provides 95% confidence intervals for the average percent of time drivers in the population would be observed not to have their hands on the wheel during various activities while the vehicle was
20. Refer to the following statement on page 396: “For example, as you can see from the reported confidence intervals, we can’t rule out the possibility that the differences in IQ at 1 and 2 years of age were in the other direction because the interval covers some negative values.” The
19. Refer to Case Study 21.1 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 21.1. 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 21.1, 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 21.2 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 can-cer 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. Explain in words that someone
*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
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 20, 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 ifa. The confidence interval did not cover 1.0.b. 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 zero.*b. 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 20, 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
*20. Refer to News Story 13 and the accompanying report on the CD, “2003 CASA National Survey of American Attitudes on Substance Abuse VIII: Teens and Parents.”a. The margin of error for the teens and for the parents are reported in the news story. What are they reported to be?b. Refer to page
19. Refer to News Story 2 in the Appendix and on the CD, “Research shows women harder hit by hangovers,” and the accompanying Original Source 2 on the CD,“Development and initial validation of the Hangover Symptoms Scale: Prevalence and correlates of hangover symptoms in college students.”
18. In a poll reported in Newsweek (16 May 1994, p. 23) one of the questions asked was, “Is the media paying too much attention to [President] Clinton’s private life, too little, or about the right amount of attention?” Results showed that 59%answered “too much,” 5% answered “too
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
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.
11. A university is contemplating switching from the quarter system to the semester system. The administration conducts a survey of a random sample of 400 students and finds that 240 of them prefer to remain on the quarter system.a. Construct a 95% confidence interval for the true proportion of all
10. Confirm that the standard deviation for sample proportions is largest when the proportion used to calculate it is .50. Do this by using other values above and below .50 and comparing the answers to what you would get using .50. Try three values above and three values below .50.
9. Find the results of a poll reported in a weekly newsmagazine such as Newsweek or Time, in a newspaper such as the New York Times, or on the Internet in which a margin of error is also reported. Explain what question was asked and what margin of error was reported; then present a 95% confidence
8. Refer to Example 6 in this chapter. It is claimed that a 95% confidence interval for the percentage of placebo-patch users who quit smoking by the eighth week covers 13% to 27%. There were 120 placebo-patch users, and 24 quit smoking by the eighth week. Verify that the confidence interval given
*7. Parade Magazine reported that “nearly 3200 readers dialed a 900 number to respond to a survey in our Jan. 8 cover story on America’s young people and violence”(19 February 1995, p. 20). Of those responding, “63.3% say they have been victims or personally know a victim of violent
6. Explain whether the width of a confidence interval would increase, decrease or remain the same as a result of each of the following changes:a. The sample size is doubled, from 400 to 800.b. The population size is doubled, from 25 million to 50 million.c. The level of confidence is lowered from
*5. What level of confidence would accompany each of the following intervals?*a. Sample proportion 1.0(SD)*b. Sample proportion 1.645(SD)c. Sample proportion 1.96(SD)d. Sample proportion 2.576(SD)
4. A telephone poll reported in Time magazine (6 February 1995, p. 24) asked 359 adult Americans the question, “Do you think Congress should maintain or repeal last year’s ban on several types of assault weapons?” Seventy-five percent responded “maintain.”a. Compute the standard deviation
3. On September 10, 1998, the “Starr Report,” alleging impeachable offenses by President Bill Clinton, was released to Congress. That evening, the Gallup Organization conducted a poll of 645 adults nationwide to assess initial reaction(reported at www.gallup.com). One of the questions asked
*2. Refer to Exercise 1. Of the 193 placebo takers, 43 reported headaches.*a. Compute a 95% confidence interval for the true population proportion that would get headaches after taking a placebo.b. Notice that a higher proportion of placebo takers than Seldane-D takers reported headaches. Use that
1. An advertisement for Seldane-D, a drug prescribed for seasonal allergic rhinitis, reported results of a double-blind study in which 374 patients took Seldane-D and 193 took a placebo (Time, 27 March 1995, p. 18). Headaches were reported as a side effect by 65 of those taking Seldane-D.a. What is
2. The purpose of this mini-project is to help you verify the Rule for Sample Means. Suppose you are interested in measuring the average amount of blood contained in the bodies of adult women, in ounces. Suppose, in truth, the population consists of the following listed values. (Each value would be
1. The goal of this mini-project is to help you verify the Rule for Sample Proportions firsthand. You will use the population represented in Figure 19.1 to do so.It contains 400 individuals, of whom 160 (40%) are —that is, carry the gene for a disease—and the remaining 240 (60%) are —that is,
18. The administration of a large university wants to use a random sample of students to measure student opinion of a new food service on campus. Admin- istrators plan to use a continuous scale from 1 to 100, where 1 is complete dissatisfaction and 100 is complete satisfaction. They know from past
*17. Suppose the population of grade-point averages (GPAs) for students at the end of their first year at a large university has a mean of 3.1 and a standard deviation of .5. Draw a picture of the frequency curve for the mean GPA of a random sample of 100 students, similar to Figure 19.6.
16. In Case Study 19.1, we learned that about 56% of American adults actually voted in the presidential election of 1992, whereas about 61% of a random sample claimed that they had voted. The size of the sample was not specified, but suppose it were based on 1600 American adults, a common size for
15. Explain whether you think the Rule for Sample Means applies to each of the following situations. If it does apply, specify the population of interest and the measurement of interest. If it does not apply, explain why not.a. A researcher is interested in what the average cholesterol level would
*14. Explain whether each of the following situations meets the conditions for which the Rule for Sample Proportions applies. If not, explain which condition is violated.*a. Unknown to the government, 10% of all cars in a certain city do not meet appropriate emissions standards. The government
*13. According to the Sacramento Bee (2 April 1998, p. F5), Americans get an average of 6 hours and 57 minutes of sleep per night. A survey of a class of 190 statistics students at a large university found that they averaged 7.1 hours of sleep the previous night, with a standard deviation of 1.95
12. Use the Rule for Sample Means to explain why it is desirable to take as large a sample as possible when trying to estimate a population value.
*11. Suppose 20% of all television viewers in the country watch a particular program.*a. For a random sample of 2500 households measured by a rating agency, describe the frequency curve for the possible sample proportions who watch the program.*b. The program will be canceled if the ratings show
10. According to USA Today (20 April 1998, Snapshot), a poll of 8709 adults taken in 1976 found that 9% believed in reincarnation, whereas a poll of 1000 adults taken in 1997 found that 25% held that belief.a. Assuming a proper random sample was used, verify that the sample proportion for the poll
9. Suppose that 35% of the students at a university favor the semester system, 60%favor the quarter system, and 5% have no preference. Is a random sample of 100 students large enough to provide convincing evidence that the quarter system is favored? Explain.
8. Suppose the population of IQ scores in the town or city where you live is bellshaped, with a mean of 105 and a standard deviation of 15. Describe the frequency curve for possible sample means that would result from random samples of 100 IQ scores.
*7. Give an example of a situation of interest to you for which the Rule for Sample Proportions would apply. Explain why the conditions allowing the rule to be applied are satisfied for your example.
6. Refer to Exercise 5. Redraw the picture under the assumption that you will collect 100 measurements instead of only 9. Discuss how the picture differs from the one in Exercise 5.
1. Draw a picture of the possible sample means you are likely to get based on your sample of nine observations. Include the intervals into which 68%, 95%, and almost all of the potential sample means will fall.
5. Suppose you are interested in estimating the average number of miles per gallon of gasoline your car can get. You calculate the miles per gallon for each of the next nine times you fill the tank. Suppose, in truth, the values for your car are bell-shaped, with a mean of 25 miles per gallon and a
*4. A recent Gallup Poll found that of 800 randomly selected drivers surveyed, 70%thought they were better-than-average drivers. In truth, in the population, only 50% of all drivers can be “better than average.”a. Draw a picture of the possible sample proportions that would result from samples
3. According to the Sacramento Bee (2 April 1998, p. F5), “A 1997–98 survey of 1027 Americans conducted by the National Sleep Foundation found that 23% of adults say they have fallen asleep at the wheel in the last year.”a. Conditions 2 and 3 needed to apply the Rule for Sample Proportions
2. Refer to Exercise 1. Suppose the truth is that .12 or 12% of the students are lefthanded, and you take a random sample of 200 students. Use the Rule for Sample Proportions to draw a picture similar to Figure 19.3, showing the possible sample proportions for this situation.
1. Suppose you want to estimate the proportion of students at your college who are left-handed. You decide to collect a random sample of 200 students and ask them which hand is dominant. Go through the conditions for which the rule for sample proportions applies (p. 358) and explain why the rule
3. Conduct a survey in which you ask 20 people the two scenarios presented in Thought Question 5 at the beginning of this chapter and discussed in Section 18.5. Record the percentage who choose alternative A over B and the percentage who choose alternative C over D.a. Report your results. Are they
2. Ask four friends to tell you their most amazing coincidence story. Use the material in this chapter to assess how surprising each of the stories is to you. Pick one of the stories and try to approximate the probability of that specific event happening to your friend.
1. Find out the sensitivity and specificity of a common medical test. Calculate the probability of a true positive for someone who tests positive with the test, assuming the rate in the population is 1 per 100; then calculate the probability assuming the rate in the population is 1 per 1000.
24. Comment on the following unusual lottery events, including a probability assessment.a. On September 11, 2002, the first anniversary of the 9/11 attack on the World Trade Center, the winning number for the New York State lottery was 911.b. To play the Maryland Pick 4 lottery, players choose four
23. Suppose you are trying to decide whether to park illegally while you attend class. If you get a ticket, the fine is $25. If you assess the probability of getting a ticket to be 1100, what is the expected value for the fine you will have to pay?Under those circumstances, explain whether you
*22. Refer to Case Study 18.2, in which the relationship between betting odds and probability of occurrence is explained.a. Suppose you are offered a bet on an outcome for which the odds are 2 to 1 and there is no handling fee. For you to have a break-even expected value of zero, what would the
21. It is time for the end-of-summer sales. One store is offering bathing suits at 50%of their usual cost, and another store is offering to sell you two for the price of one. Assuming the suits originally all cost the same amount, which store is offering a better deal? Explain.
*20. We learned in this chapter that one idea researchers have tested was that when forced to make a decision, people choose the alternative that yields the highest expected value.*a. If that were the case, explain which of the following two choices people would make:Choice A: Accept a gift of
19. Explain why it would be much more surprising if someone were to flip a coin and get six heads in a row after telling you they were going to do so than it would be to simply watch them flip the coin six times and observe six heads in a row.
18. If you wanted to pretend that you could do psychic readings, you could perform“cold readings” by inviting people you do not know to allow you to tell them about themselves. You would then make a series of statements like“I see that there is some distance between you and your mother that
*17. Suppose a friend reports that she has just had a string of “bad luck” with her car.She had three major problems in as many months and now has replaced many of the worn parts with new ones. She concludes that it is her turn to be lucky and that she shouldn’t have any more problems for a
16. Suppose the sensitivity of a test is .90. Give either the false positive or the false negative rate for the test, and explain which you are providing. Could you provide the other one without additional information? Explain.
15. A statistics professor once made a big blunder by announcing to his class of about 50 students that he was fairly certain that someone in the room would share his birthday. We have already learned that there is a 97% chance that there will be 2 people in a room of 50 with a common birthday.
14. Explain why the story about George D. Bryson, reported in Example 1 in this chapter, is not all that surprising.
13. Using the data in Table 18.1, give numerical values and explain the meaning of the sensitivity and the specificity of the test.
*12. Using the data in Table 18.1 about a hypothetical population of 100,000 women tested for breast cancer, find the probability of each of the following events:*a. A woman whose test shows a malignant lump actually has a benign lump.*b. A woman who actually has a benign lump has a test that shows
11. You are at a casino with a friend, playing a game in which dice are involved.Your friend has just lost six times in a row. She is convinced that she will win on the next bet because she claims that, by the law of averages, it’s her turn to win. She explains to you that the probability of
10. Suppose a rare disease occurs in about 1 out of 1000 people who are like you.A test for the disease has sensitivity of 95% and specificity of 90%. Using the technique described in this chapter, compute the probability that you actually have the disease, given that your test results are positive.
*9. Many people claim that they can often predict who is on the other end of the phone when it rings. Do you think that phenomenon has a normal explanation?Explain.
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