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Seeing Through Statistics 4th Edition Jessica M.Utts - Solutions

In addition to the overall CPI, the BLS reports the index for the subcategories. The overall CPI in May, 2013, was 232.9. Following are the values for some of the subcategories, taken from the CPI website: Dairy products........... 216.3 Fruits, vegetables............ 289.2 Alcoholic
Table 18.6 shows the amounts Americans spent for medical care, per capita, between 1987 and 1993 (World Almanac and Book of Facts, 1995, p. 128 and Census Bureau).a. Create a €œmedical care index€ for each of these years, using 1987 as a base.b. Comment on how the cost of medical care
An article in the Sacramento Bee (Stafford, 2003) on July 7, 2003, reported that the current minimum wage at that time was only $ 5.15 an hour and that it had not kept pace with inflation. The Consumer Price Index at the time (the end of June, 2003) was 183.7. a. One of the quotes in the article
Find out the current minimum wage and the current Consumer Price Index. (These were available as of July, 2013, at the websites www.dol.gov/dol/topic/wages/ and www.bls.gov/cpi/, respectively.) Determine what the minimum wage should be at the current time if it had kept pace with inflation from a.
The United States Census Bureau, Statistical Abstract of the United States 1999 (p. 877) contains a table listing median family income for each year from 1947 to 1997. The incomes are presented “in current dollars” and “in constant (1997) dollars.” As an example, the median income in 1985
In explaining why it is a costly mistake to have the CPI overestimate inflation, the Associated Press (20 October 1994) reported, “ Every 1 percentage point increase in the CPI raises the federal budget deficit by an estimated $ 6.5 billion.” Explain why that would happen.
Many U.S. government payments, such as Social Security benefits, are increased each year by the percentage change in the CPI. In 1995, the government started discussions about lowering these increases or changing the way the CPI is calculated.
Most news accounts of the Consumer Price Index report the percentage change in the CPI from the previous month rather than the value of the CPI itself. Why do you think that is the case?
Recall from Chapter 9 that time series (such as the CPI) have three nonrandom components. Which of the three nonrandom components (trend, seasonal, or cycles) is likely to contribute the most to the unadjusted Consumer Price Index? Explain.
The Bureau of Labor Statistics reports that one use of the Consumer Price Index is to periodically adjust the federal income tax structure, which sets higher tax rates for higher income brackets. According to the BLS, “these adjustments prevent inflation- induced increases in tax rates, an effect
In February of 1994, the Index of Leading Economic Indicators dropped slightly, and economists blamed it on unusually severe winter weather that month. Examine the 10 series that make up the Index of Leading Economic Indicators. Choose at least two of the series to support the explanation that the
A paperback novel cost $ 3.49 in 1981, $ 6.99 in 1995, and $ 14.00 in 2013. Compute a “paperback novel price index” for 1995 and 2013 using 1981 as the base year. In words that can be understood by someone with no training in statistics, explain what the resulting numbers mean.
The Dow Jones Industrial Average reached a high of $ 7801.63 on December 29, 1997. Recall from Example 18.4 that it reached a high of $ 1003 on November 14, 1972. The Consumer Price Index for November 1972 was 42.4; for December 1997, it was 161.3. By what percentage did the high in the DJIA
The CPI in July, 1977, was 60.9; in July, 1994, it was 148.4. a. The salary of the governor of California in July, 1977, was $ 49,100; in July 1994, it was $ 120,000. Compute what the July, 1977, salary would be in July, 1994, adjusted for inflation, and compare it with the actual salary in July,
As mentioned in this chapter, both the base year and the relative weights used for the Consumer Price Index are periodically updated. a. Why is it important to update the relative weights used for the CPI? b. Explain why the base year is periodically updated.
The CPIs at the start of each decade from 1940 to 2010 were are shown in Table 18.5.a. Determine the percentage increase in the CPI for each decade.b. During which decade was inflation the highest, as measured by the percentage change in the CPI?c. During which decade was inflation the lowest, as
Find a news story that reports on current values for one of the indexes discussed in this chapter. Discuss the news report in the context of what you have learned in this chapter. For example, does the report contain any information that might be misleading to an uneducated reader? Does it omit any
In addition to the Dow Jones Industrial Average, there are other indicators of fluctuation in stock prices. Two examples are the New York Stock Exchange Composite Index and the Standard and Poor’s 500. Choose a stock index (other than the Dow Jones), and write a report about it. Include whether
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. 411) and explain why the rule would
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.
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 are
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
Suppose the population of IQ scores in the town or city where you live is bell-shaped, 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.
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. You are interested in knowing what proportion of days in typical years have rain or snow in the area where you live. For the
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 wants to
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 be
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 university wants to know the average income of its alumni. Staff members
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 19.5.
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 such
Suppose the truth is that .12, or 12%, of the students are left-handed, 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.
A Gallup Poll found that of 800 randomly selected drivers surveyed, 70% thought they were better-than-average drivers. In truth, in the population, no more than 50% of all drivers can be “better than average,” assuming “average” is equivalent to the median level of skill. a. Draw a
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
Refer to Exercise 4. Redraw the picture under the assumption that you will collect 100 measurements instead of only nine. Discuss how the picture differs from the one in Exercise 4.In exercise 4, Suppose you are interested in estimating the average number of miles per gallon of gasoline your car
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.
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
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 less
The goal of this mini-project is to help you verify the Rule for Sample Proportions firsthand, using a physical simulation. 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
The purpose of this mini-project is to help you verify the Rule for Sample Means, using a physical simulation. 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
Carry out the simulation in Mini-Project # 1 using a computer or website instead of physically doing so. Go through the same steps and answer the same questions.
Carry out the simulation in Mini-Project # 2 using a computer or website instead of physically doing so. Go through the same steps and answer the same questions.
One of the questions asked in a Gallup poll taken in May, 2012, in the United States was: “All in all, if you had your choice, would you want to be rich, or not?” (Newport, 2012). (A previous question had asked respondents if they thought they were rich, and the 2% who said yes were not
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.
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
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
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. It
In a 2008 Scripps Howard News/ Ohio University survey of 1003 randomly selected adults, 56% said that it is either very or somewhat likely that there is intelligent life on other planets (www.scrippsnews.com/node/34758). For each part, use the desired confidence level to find a confidence
In Example 20.5, 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 rather than the 95% confidence interval.
Refer to the formula for a confidence interval in the Focus on Formulas section. a. Write the formula for a 90% confidence interval for a proportion. b. Refer to Example 20.6. Construct a 90% confidence interval for the proportion of smokers who would quit after 8 weeks using a nicotine patch. c.
Another question asked in the Gallup poll in Exercise 1 was: “Do you think that rich people in America today are happier than you, less happy, or about the same?” (Newport, 2012). Of the 1008 respondents, only 11% said “happier,” 27% said “less happy,” 57% said “about the same,” and
One of the questions asked in a Pew Research Center/ USA Today poll taken in June, 2013, was: “Overall, do you approve or disapprove of the government’s collection of telephone and internet data as part of antiterrorism efforts?” (www.pollingreport.com/terror.htm).
In each situation, explain why you think that the sample proportion should or should not be used to estimate the population proportion. a. An Internet news organization asks visitors to its website to respond to the question: “Are you satisfied with the president’s job performance?” Of 3500
An advertisement for SeldaneD, a (now discontinued) drug prescribed for seasonal allergic rhinitis, reported results of a double-blinda 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
Refer to Exercise 22. 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
Suppose 200 different researchers all randomly select samples of 400 individuals from a population. Each researcher uses his or her sample to compute a 95% confidence interval for the proportion that has blue eyes in the population. About how many of the confidence intervals will cover the
Refer to News Story 2 in the Appendix and on the book’s website, “Research shows women harder hit by hangovers,” and the accompanying Original Source 2 on the website, “Development and initial validation of the Hangover Symptoms Scale: Prevalence and correlates of hangover symptoms in
Refer to News Story 13 and the accompanying report on the book’s website, “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.
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 was:
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 error that
What level of confidence would accompany each of the following intervals? a. Sample proportion ± 1.0(SEP) b. Sample proportion ± 1.645(SEP) c. Sample proportion ± 1.96(SEP) d. Sample proportion ± 2.576(SEP)
Use the Empirical Rule to specify what level of confidence would accompany each of the following confidence intervals. a. Sample proportion ± 1(SEP) b. Sample proportion ± 2(SEP) c. Sample proportion ± 3(SEP)
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
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
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
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 results,
In this chapter technical detail were presented for finding a t-multiplier for constructing a confidence interval for a population mean. Use appropriate software, a calculator, or a website to find a confidence interval for the population mean for the following situations. Use the t-multiplier in
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 day
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 =
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 case study, explain why we cannot use the method presented in Section 21.2 to compare baseline symptom scores with third-cycle symptom scores for the calcium-treated
Parts (a) through (d) below provide additional results for Case Study 21.1. For each of the parts, compute an approximate 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
In Chapter 20, we learned that to compute an approximate 90% confidence interval, the appropriate multiplier is 1.645 instead of 2.0. This works for confidence intervals for one mean or the difference in two means as well. Consult Table 21.2 on page 458 to find the means and standard errors for the
Explain the difference between a population mean and a sample mean using one of the studies discussed in the chapter as an example.
The 200 men in the sample had a mean height of 68.2 inches, with a standard deviation of 2.7 inches. The 200 women had a mean height of 63.1 inches, with a standard deviation of 2.5 inches. Assuming these were independent samples, compute an approximate 95% confidence interval for the mean
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 study,
Refer to the following statement on page 458: “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 statement
a. The confidence interval accompanying “Reading/writing” is from 4.24% to 34.39%. Write a few sentences interpreting this interval that would be understood by someone with no training in statistics. Make sure you are clear about the population to which the result applies. b. Repeat part (a)
Refer to Original Source 9 on the companion website, “Suicide Rates in Clinical Trials of SS-RIs, 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
The 95% confidence interval for “All Causes” is 1.06 to 1.37. Explain what this interval means in a few sentences that would be understood by some-one with no training in statistics. Make sure your explanation applies to the correct population.
Confidence intervals are given for the relative risk of death for five specific causes of death, as follows: Circulatory (1.02 to 1.45), Cancer (0.83 to 1.37), Digestive (0.98 to 4.03), Respiratory (0.92, 3.02) and External (0.60 to 2.12). For which of these causes can it be concluded that the risk
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 66
Refer to the link to Original Source 11 on the companion website, “Driving impairment due to sleepiness is exacerbated by low alcohol in-take.” (If the link no longer works, do a search on the title of the article to locate it.) Table 1 on the top of page 691 of the article presents mean blood
Table 1 on page 200 of Original Source 18, “Birth weight and cognitive function in the British 1946 birth cohort: longitudinal population based study” (link available on the companion website), provides 95% confidence intervals for the difference in mean standardized cognitive scores for
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 1.0. b. The confidence interval did cover 1.0.
Ever since President John F. Kennedy was assassinated in 1963, there has been speculation about whether there was a single assassin or more than one. Periodically, public opinion polls ask this question: “Turning now to the assassination of John F. Kennedy in 1963—Do you think that one man was
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
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 an approximate 95% confidence interval for the difference in the means of the
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 5 0.35 b. p-value 5 0.04
For the research described in Case Study 6.2, the goal was to find out if eating breakfast cereal was associated with a reduction in body mass index ( BMI) for children (Frantzen et al., 2013). Although the analysis used by the researchers was somewhat complicated, for simplicity in this exercise,
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
A report in the Davis (CA) Enterprise (6 April 1994, p. A11) 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
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 null standard error for the potential sample
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 FDA
If we had conducted the hypothesis test, the resulting p-value would be 0.01. Explain what the p-value represents for this example.
In Case Study 1.2 and in Chapters 12 and 13, 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
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
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 did
a. The participants in the study were five capuchin monkeys. To what population do you think the results apply? b. The researchers were interested in comparing the proportion of times the monkeys would cooperate by trading the token for the cucumber after observing another monkey doing the same,
See the information for Exercises 23 and 24 provided on page 493. Refer to the quote that begins with “Despite the small number . . .” a. Based on the quote, what do you know about the p-value? b. Based on the quote, what level of significance are the researchers using? c. What conclusion
In Original Source 2 on the companion website, “Development and initial validation of the Hangover Symptoms Scale: Prevalence and correlates of hangover symptoms in college students,” one of the questions was how many times respondents had experienced at least one hangover symptom in the past
Refer to the previous exercise. Repeat the test for women only. Refer to Table 3 of the paper for the data.
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

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