In 2010, shortly before that year’s midterm elections, when Americans were dissatisfied with government and the Tea Party movement was emerging as a political force, 58% of American adults thought that a third major party was needed. In a recent Gallup poll, 60% of 1028 Americans felt the same way. At the 10% significance level, do the data provide sufficient evidence to conclude that the percentage of all American adults who now think that a third major party is needed has changed from that in 2010?
> An article, titled “We’re Happiest at 74; It’s All Downhill till 40, Then Life Gets Better, Say Scientists,” included a graph, similar to the following one, of a happiness scale versus age. The article argues that happiness decreases until the age of 46
> Suppose that bivariate data are to be grouped into a contingency table. Determine the number of cells that the contingency table will have if the numbers of possible values for the two variables are a. two and three. b. four and three. c. m and n.
> What are the small boxes inside the heavy lines of a contingency table called?
> Identify the type of table that is used to group bivariate data.
> The chi-square goodness-of-fit test provides a method for performing a hypothesis test about the distribution of a variable that has c possible values. If the number of possible values is 2, that is, c = 2, the chi-square goodness-of-fit test is equivale
> Table showed the calculated sums of the observed frequencies, the expected frequencies, and their differences. Strictly speaking, those sums are not needed. However, they serve as a check for computational errors. a. In general, what common value should
> One probability model for child gender is that a boy or a girl is equally likely to be born. If that model is correct, then, for a two-child family, the probabilities are 0.25, 0.50, and 0.25 of two girls, one girl and one boy, and two boys, respectively
> Arabidopsis is a genus of flowering plant related to cabbage. A variegated mutant of the Arabidopsis has yellow streaks or marks. E. Miura et al. studied the origin of this variegated mutant in the article “The Balance between Protein Synthesis and Degra
> The World Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919–1921 World Series, when it was a best of nine). Thus it takes at least four games and no more than seven games to establish a winner. If two teams are eve
> A project exploring the bottled-water phenomenon and preference of water types was conducted by researchers M. Lunsford and A. Fink in the article “Water Taste Test Data” (Journal of Statistics Education, Vol. 18, No. 1). One hundred nine subjects partic
> Consider two χ2-curves with degrees of freedom 12 and 20, respectively. Which one more closely resembles a normal curve? Explain your answer.
> Drunk-driving fatalities represent the total number of people (occupants and non-occupants) killed in motor vehicle traffic crashes in which at least one driver had a blood alcohol content (BAC) of 0.08 or higher. The following graph is based on data pub
> A gambler thinks a die may be loaded, that is, that the six numbers are not equally likely. To test his suspicion, he rolled the die 150 times and obtained the data shown in the following table. Do the data provide sufficient evidence to conclude that th
> An American roulette wheel contains 18 red numbers, 18 black numbers, and 2 green numbers. The following table shows the frequency with which the ball landed on each color in 200 trials. At the 5% significance level, do the data suggest that the wheel is
> Observing that the proportion of blue M&Ms in his bowl of candy appeared to be less than that of the other colors, R. Fricker, Jr., decided to compare the color distribution in randomly chosen bags of M&Ms to the theoretical distribution reported by M&M/
> The report Controlling Road Rage: A Literature Review and Pilot Study was prepared for the AAA Foundation for Traffic Safety by D. Rathbone and J. Huckabee. The authors discussed the results of a literature review and pilot study on how to prevent aggres
> The Higher Education Research Institute of the University of California, Los Angeles, publishes information on characteristics of incoming college freshmen in The American Freshman. In 2000, 27.7% of incoming freshmen characterized their political views
> According to the U.S. Census Bureau publication Demographic Profiles, a relative-frequency distribution of the U.S. resident population by region in 2000 was as follows. A simple random sample of this year’s U.S. residents gave the following frequency di
> We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distri
> We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distri
> Of the quantities p1, p2, x1, x2, pˆ1, pˆ2, and pˆp, a. which represent parameters and which represent statistics? b. which are fixed numbers and which are variables?
> We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distri
> The Federal Reserve System publishes weekly figures of M2 money supply in the document Money Stock Measures. M2 includes such things as cash in circulation, deposits in checking accounts, nonbank traveler’s checks, accounts such as savings deposits, and
> Consider a hypothesis test for two population proportions with the null hypothesis H0: p1 = p2. What parameter is being estimated by the a. sample proportion pˆ1? b. sample proportion pˆ2? c. pooled sample proportion pˆp?
> We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distri
> Industry Research polled teenagers on sunscreen use. The survey revealed that 46% of teenage girls and 30% of teenage boys regularly use sunscreen before going out in the sun. a. Identify the specified attribute. b. Identify the two populations. c. Are t
> How do you identify different chi-square distributions?
> In an ABC Global Kids Study, conducted by Roper Starch Worldwide, Inc., estimates were made in various countries of the percentage of children who attend church at least once a week. Two of the countries in the survey were the United States and Germany.
> We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distri
> Explain the basic idea for performing a hypothesis test, based on independent samples, to compare two population proportions.
> We have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distri
> In the article “Drowning Deaths of Zero to Five Year Old Children in Victorian Dams, 1989–2001” (Australian Journal of Rural Health, Vol. 13, Issue 5, pp. 300–308), L. Bugeja and R. Franklin examined drowning deaths of young children in Victorian dams to
> According to Current Housing Reports, published by the U.S. Census Bureau, the primary heating fuel for all occupied housing units is distributed as follows. Suppose that you want to determine whether the distribution of primary heating fuel for occupied
> The U.S. Census Bureau publishes data on the population of the United States by race and Hispanic origin in American Community Survey. From that document, we constructed the following bar chart. Note that people who are Hispanic may be of any race, and p
> We have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fit test and the sample size. Decide whether Assumptions 1 and 2 for using that test are satisfied. Sample size: n = 100. Relative frequencies: 0.44, 0.25, 0.30,
> A Harris Interactive survey found that 92.0%of 1001 American adults said they always wash up after using the bathroom. a. At the 5% significance level, do the data provide sufficient evidence to conclude that more than 9 of 10 Americans always wash up af
> We have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fit test and the sample size. Decide whether Assumptions 1 and 2 for using that test are satisfied. Sample size: n = 50. Relative frequencies: 0.22, 0.22, 0.25, 0
> In the article “Prothrombotic Factors in Children With Stroke or Porencephaly” (Pediatrics Journal, Vol. 116, Issue 2, pp. 447–453), J. Lynch et al. compared differences and similarities in children with arterial ischemic stroke and porencephaly. Three c
> We have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fit test and the sample size. Decide whether Assumptions 1 and 2 for using that test are satisfied. Sample size: n = 50. Relative frequencies: 0.22, 0.21, 0.25, 0
> In a national poll, 1053 U.S. adults were asked, “As you may know, Congress is considering a new economic stimulus package of at least 800 billion dollars. Do you favor or oppose Congress passing this legislation?” Of those sampled, 548 favored passage.
> We have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fit test and the sample size. Decide whether Assumptions 1 and 2 for using that test are satisfied. Sample size: n = 50. Relative frequencies: 0.20, 0.20, 0.25, 0
> Of the 38 numbers on an American roulette wheel, 18 are red, 18 are black, and 2 are green. If the wheel is balanced, the probability of the ball landing on red is 18/38 = 0.474. A gambler has been studying a roulette wheel. If the wheel is out of balanc
> We have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fit test and the sample size. Decide whether Assumptions 1 and 2 for using that test are satisfied. Sample size: n = 50. Relative frequencies: 0.65, 0.30, 0.05.
> This exercise involves the use of an unrealistically small population to provide a concrete illustration for the exact distribution of a sample proportion. A population consists of three men and two women. The first names of the men are Jose, Pete, and C
> Each year the director of the reading program in a school district administers a standard test of reading skills. Then the director compares the average score for his district with the national average. Figure 2.20 was presented to the school board in th
> We have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fit test and the sample size. Decide whether Assumptions 1 and 2 for using that test are satisfied. Sample size: n = 100. Relative frequencies: 0.65, 0.30, 0.05.
> Labor Day was created by the U.S. labor movement over 100 years ago. It was subsequently adopted by most states as an official holiday. In a poll by Gallup, 1003 randomly selected adults were asked whether they approve of labor unions; 65% said yes. a. I
> In 2012, 15.9% of all U.S. families had incomes below the poverty level, as reported by the U.S. Census Bureau in American Community Survey. During that same year, of 400 randomly selected Wyoming families, 50 had incomes below the poverty level. At the
> P. Noakes et al. researched the effects of fatty acids found in oily fish on lowering the risk of allergic disease in the article “Increased Intake of Oily Fish in Pregnancy: Effects on Neonatal Immune Responses and on Clinical Outcomes in Infants at 6 M
> A poll conducted by Gallup asked American adults about vegetarianism. This problem is based on that poll. Of independent random samples of 500 men and 512 women, 20 of the men and 36 of the women said they were vegetarians. At the 5% significance level d
> The Arizona Republic conducted a telephone poll of 758 Arizona adults who celebrate Christmas. The question asked was, “In your family, do you open presents on Christmas Eve or Christmas Day?” Of those surveyed, 394 said they wait until Christmas Day. a.
> Scoliosis is a condition involving curvature of the spine. In a study by A. Nachemson and L. Peterson, reported in the Journal of Bone and Joint Surgery (Vol. 77, Issue 6, pp. 815–822), 286 girls aged 10 to 15 years were followed to determine the effects
> Gallup conducted a national survey of 1008 American adults, asking “As you may know, as part of its efforts to investigate terrorism, a federal government agency obtained records from larger U.S. telephone and Internet companies in order to compile telep
> The Quinnipiac University Poll conducts nationwide surveys as a public service and for research. This problem is based on the results of one such poll that asked independent random samples of American adults in urban, suburban, and rural regions, “Do you
> The Times Higher Education “World University Rankings” presents global university performance tables to judge world class universities on the basis of teaching, research, knowledge transfer, and international outlook. The rankings employ 13 carefully cal
> We have given the number of successes and the sample size for a simple random sample from a population. In each case, do the following. a. Determine the sample proportion. b. Decide whether using the one-proportion z-test is appropriate. c. If appropriat
> The Quinnipiac University Poll conducts nationwide surveys as a public service and for research. This problem is based on the results of one such poll. Independent simple random samples of 300 residents each in red (predominantly Republican), blue (predo
> We have given the number of successes and the sample size for a simple random sample from a population. In each case, do the following. a. Determine the sample proportion. b. Decide whether using the one-proportion z-test is appropriate. c. If appropriat
> The U.S. Census Bureau compiles data on the U.S. population by region and race and publishes its findings in Current Population Reports. Independent simple random samples of residents in the four U.S. regions gave the following data on race. At the 1% si
> We have given the number of successes and the sample size for a simple random sample from a population. In each case, do the following. a. Determine the sample proportion. b. Decide whether using the one-proportion z-test is appropriate. c. If appropriat
> In the article “The Influence of Theme as Slot Machine Attribute on Casino Gamers Decision-Making” (American Journal of Applied Sciences, Vol. 10, No. 7, pp. 734–739), E. Wannenburg et al. explore the effects of theme on slot-machine gamers. Independent
> We have given the number of successes and the sample size for a simple random sample from a population. In each case, do the following. a. Determine the sample proportion. b. Decide whether using the one-proportion z-test is appropriate. c. If appropriat
> Self-concept can be defined as the general view of oneself in terms of personal value and capabilities. A study of whether visual impairment affects self-concept was reported in the article “An Exploration into Self Concept: A Comparative Analysis betwee
> We have given the number of successes and the sample size for a simple random sample from a population. In each case, do the following. a. Determine the sample proportion. b. Decide whether using the one-proportion z-test is appropriate. c. If appropriat
> A chi-square homogeneity test is to be conducted to decide whether four populations are nonhomogeneous with respect to a variable that has eight possible values. What are the degrees of freedom for the χ2-statistic?
> This exercise deals with truncated graphs. a. What is a truncated graph? b. Give a legitimate motive for truncating the axis of a graph. c. If you have a legitimate motive for truncating the axis of a graph, how can you correctly obtain that objective wi
> Explain the relationships among the sample proportion, the number of successes in the sample, and the sample size.
> Are the observed frequencies variables? What about the expected frequencies? Explain your answers.
> We have given the number of successes and the sample size for a simple random sample from a population. In each case, do the following. a. Determine the sample proportion. b. Decide whether using the one-proportion z-test is appropriate. c. If appropriat
> What is meant by saying that a variable has a chi-square distribution?
> In the February 2013 article “Offshore Drilling Support High as Deepwater Horizon Oil Spill Trial Opens,” E. Swanson reported on a HuffPost and YouGov poll that asked Americans what they think about increased offshore drilling for oil and natural gas. Of
> In a New York Times article “More Mothers Breast-Feed, in First Months at Least,” G. Harris reported that 77% of new mothers breast-feed their infants at least briefly, the highest rate seen in the United States in more than a decade. His report was base
> A Pew Internet & American Life Project examined Internet social networking. Among a sample of 929 online adults 18–29 years old, 836 said they use social networking sites. Determine a 95% confidence interval for the percentage of all online adults 18–29
> A poll by Gallup asked, “If you won 10 million dollars in the lottery, would you continue to work or stop working?” Of the 1039 American adults surveyed, 707 said that they would continue working. Obtain a 95% confidence interval for the proportion of al
> We have given the number of successes and the sample size for a simple random sample from a population. In each case, a. use the one-proportion plus-four z-interval procedure to find the required confidence interval. b. compare your result with the corre
> We have given the number of successes and the sample size for a simple random sample from a population. In each case, a. use the one-proportion plus-four z-interval procedure to find the required confidence interval. b. compare your result with the corre
> Give one reason why constructing and reading graphs and charts carefully is important.
> According to a study published in the Journal of the American Public Health Association, lefthanded people do not die at an earlier age than right-handed people, contrary to the conclusion of a highly publicized report done 2 years earlier. The investiga
> We have given the number of successes and the sample size for a simple random sample from a population. In each case, a. use the one-proportion plus-four z-interval procedure to find the required confidence interval. b. compare your result with the corre
> We have given the number of successes and the sample size for a simple random sample from a population. In each case, a. use the one-proportion plus-four z-interval procedure to find the required confidence interval. b. compare your result with the corre
> We have given the number of successes and the sample size for a simple random sample from a population. In each case, a. use the one-proportion plus-four z-interval procedure to find the required confidence interval. b. compare your result with the corre
> For what is the phrase “number of failures” an abbreviation?
> We have given the number of successes and the sample size for a simple random sample from a population. In each case, a. use the one-proportion plus-four z-interval procedure to find the required confidence interval. b. compare your result with the corre
> In discussing the sample size required for obtaining a confidence interval with a prescribed confidence level and margin of error, we made the following statement: “. . . we should be aware that, if the observed value of pˆ is closer to 0.5 than is our e
> In discussing the sample size required for obtaining a confidence interval with a prescribed confidence level and margin of error, we made the following statement: “If we have in mind a likely range for the observed value of pˆ, then, in light of Fig. 11
> What important theorem in statistics implies that, for a large sample size, the possible sample proportions of that size have approximately a normal distribution?
> A poll conducted by Gallup in December 2013 asked a sample of American adults whether they approved of the way President Obama was doing his job; 42% said yes, with a margin of error of plus or minus 3 percentage points. During that same time period, Qui
> On Thursday, June 13, 1996, then Arizona Governor Fife Symington was indicted on 23 counts of fraud and extortion. Just hours after the federal prosecutors announced the indictment, several polls were conducted of Arizonans asking whether they thought Sy
> One of the most important distributions in statistics is the standard normal distribution. a. Use the technology of your choice to generate a sample of 3000 observations from a variable that has the standard normal distribution. b. Use the technology of
> A company manufactures goods that are sold exclusively by mail order. The director of market research needed to test market a new product. She planned to send brochures to a random sample of households and use the proportion of orders obtained as an esti
> Refer to Exercise 11.54. a. Find the margin of error for the estimate of the percentage. b. Obtain a sample size that will ensure a margin of error of at most 5 percentage points for a 90% confidence interval without making a guess for the observed value
> Refer to Exercise 11.53. a. Find the margin of error for the estimate of the percentage. b. Obtain a sample size that will ensure a margin of error of at most 1.5 percentage points for a 99% confidence interval without making a guess for the observed val
> Refer to Exercise 11.52. a. Find the margin of error for the estimate of p. b. Obtain a sample size that will ensure a margin of error of at most 0.02 for a 95% confidence interval without making a guess for the observed value of pˆ. c. Find a 95% confid
> Regarding the phrase “number of successes”: a. For what is it an abbreviation? b. What symbol is used for it?
> Refer to Exercise 11.51. a. Determine the margin of error for the estimate of p. b. Obtain a sample size that will ensure a margin of error of at most 0.01 for a 95% confidence interval without making a guess for the observed value of pˆ. c. Find a 95% c
> According to the Internal Revenue Service, among people entitled to tax refunds, those who file online receive their refunds twice as fast as paper filers. A study conducted by International Communications Research (ICR) of Media, Pennsylvania, found tha
> In a nationwide survey, conducted by Pulse Opinion Research, LLC for Rasmussen Reports, a sample of American adults were asked whether they favor a plan to break up the 12 megabanks, which currently control about 69% of the banking industry; 50% of those
> The infant mortality rate (IMR) is the number of infant deaths per 1000 live births. Suppose that you have been commissioned to estimate the IMR in Singapore. From a random sample of 1109 live births in Singapore, you find that 0.361% of them resulted in
> Suppose that you have been hired to estimate the percentage of adults in your state who are literate. You take a random sample of 100 adults and find that 96 are literate. You then obtain a 95% confidence interval of or 0.922 to 0.998. From it you conclu
> In this exercise, use technology to work Exercise 2.159, as follows: a. Use the technology of your choice to obtain 50 random integers between 0 and 9. b. Use the technology of your choice to get a relative-frequency histogram based on single-value group
