Solution: It is hypothesized that when homing pigeons are

Samples of both surface soil and subsoil were taken from eight randomly selected agricultural locations in a particular county. The soil samples were analyzed to determine both surface pH and subsoil pH, with the results shown in the accompanying table. Location 1 2 3 45678 Surface pH 6.55 5.98 5.59 6.17 5.92 6.18 6.43 5.68 Subsoil pH 6.78 6.14 5.80 5.91 6.10 6.01 6.18 5.88 a. Compute a 90% confidence interval for the true average difference between surface and subsoil pH for agricultural land in this county. b. What assumptions are necessary to validate the interval in Part (a)?

From the given information in each case below, state what you know about the P-value for a chi-square test and give the conclusion for a significance level of a
.01. a. X2
7.5, df
2 d. X2
21.3, df
4 b. X2
13.0, df
6 e. X2
5.0, df
3

A particular paperback book is published in a choice of four different covers. A certain bookstore keeps copies of each cover on its racks. To test the hypothesis that sales are equally divided among the four choices, a random sample of 100 purchases is identified.a. If the resulting X2 value were 6.4, what conclusion would you reach when using a test with significance level .05? b. What conclusion would be appropriate at significance level .01 if X2
15.3? c. If there were six different covers rather than just four, what would you conclude if X2
13.7 and a test with a
.05 was used?

Packages of mixed nuts made by a certain company contain four types of nuts. The percentages of nuts of Types 1, 2, 3, and 4 are supposed to be 40%, 30%, 20%, and 10%, respectively. A random sample of nuts is selected, and each one is categorized by type. a. If the sample size is 200 and the resulting test statistic value is X2
19.0, what conclusion would be appropriate for a significance level of .001? b. If the random sample had consisted of only 40 nuts, would you use the chi-square test here? Explain your reasoning.

The paper Cigarette Tar Yields in Relation to Mortality from Lung Cancer in the Cancer Prevention Study II Prospective Cohort (British Medical Journal [2004]: 7279) included the accompanying data on the tar level of cigarettes smoked for a sample of male smokers who subsequently died of lung cancer. Tar Level Frequency 07 mg 103 814 mg 378 1521 mg 563 22 mg 150 Assume it is reasonable to regard the sample as representative of male smokers who die of lung cancer. Is there convincing evidence that the proportion of male smoker lung cancer deaths is not the same for the four given tar level categories?

The paper referenced in the previous exercise also gave the accompanying data on the age at which smoking started for a sample of 1031 men who smoked low-tar cigarettes. a. Use a chi-square goodness-of-fit test to test the null hypothesis H0: p1
.25, p2
.2, p3
.3, p4
.25, where p1
proportion of male low-tar cigarette smokers who started smoking before age 16, and p2, p3, and p4 are defined in a similar way for the other three age groups. b. The null hypothesis from Part (a) specifies that half of male smokers of low-tar cigarettes began smoking between the ages of 16 and 20. Explain why p2
.2 and p3
.3 is consistent with the ages between 16 and 20 being equally likely to be when smoking started.

The report Fatality Facts 2004: Bicycles (Insurance Institute, 2004) included the following table classifying 715 fatal bicycle accidents according to time of day the accident occurred. a. Assume it is reasonable to regard the 715 bicycle accidents summarized in the table as a random sample of fatal bicycle accidents in 2004. Do these data support the hypothesis that fatal bicycle accidents are not equally likely to occur in each of the 3-hour time periods used to construct the table? Test the relevant hypotheses using a significance level of .05. b. Suppose a safety office proposes that bicycle fatalities are twice as likely to occur between noon and midnight as during midnight to noon and suggests the following hypothesis: H0: p1
1/3, p2
2/3, where p1 is the proportion of accidents occurring between midnight and noon and p2 is the proportion occurring between noon and midnight. Do the given data provide evidence against this hypothesis, or are the data consistent with it? Justify your answer with an appropriate test. (Hint: Use the data to construct a one-way table with just two time categories.)

The report referenced in the previous exercise (Fatality Facts 2004: Bicycles) also classified 719 fatal bicycle accidents according to the month in which the accident occurred, resulting in the accompanying table. Number of Month Accidents January 38 February 32 March 43 April 59 May 78 June 74 July 98 August 85 September 64 October 66 November 42 December 40 a. Use the given data to test the null hypothesis H0: p1
1/12, p2
1/12, . . . , p12
1/12, where p1 is the proportion of fatal bicycle accidents that occur in January, p2 is the proportion for February, and so on. Use a significance level of .01. b. The null hypothesis in Part (a) specifies that fatal accidents were equally likely to occur in any of the 12 months. But not all months have the same number of days. What null and alternative hypotheses would you test to determine if some months are riskier than others if you wanted to take differing month lengths into account? (Hint: 2004 was a leap year, with 366 days.) c. Test the hypotheses proposed in Part (b) using a .05 significance level.

Each observation in a random sample of 100 bicycle accidents resulting in death was classified according to the day of the week on which the accident occurred. Data consistent with information given on the web site www.highwaysafety.com are given in the following table Day of Week Frequency Sunday 14 Monday 13 Tuesday 12 Wednesday 15 Thursday 14 Friday 17 Saturday 15 Based on these data, is it reasonable to conclude that the proportion of accidents is not the same for all days of the week? Use a
.05.

The color vision of birds plays a role in their foraging behavior: Birds use color to select and avoid certain types of food. The authors of the article Colour Avoidance in Northern Bobwhites: Effects of Age, Sex, and Previous Experience (Animal Behaviour [1995]: 519526) studied the pecking behavior of 1-day-old bobwhites. In an area painted white, they inserted four pins with different colored heads. The color of the pin chosen on the birds first peck was noted for each of 33 bobwhites, resulting in the accompanying table. Color First Peck Frequency Blue 16 Green 8 Yellow 6 Red 3 Do the data provide evidence of a color preference? Test using a
.01.

An article about the California lottery that appeared in the San Luis Obispo Tribune (Dec. 15, 1999) gave the following information on the age distribution of adults in California: 35% are between 18 and 34 years old, 51% are between 35 and 64 years old, and 14% are 65 years old or older. The article also gave information on the age distribution of those who purchase lottery tickets. The following table is consistent with the values given in the article: Age of Purchaser Frequency 1834 36 3564 130 65 and over 34 Suppose that the data resulted from a random sample of 200 lottery ticket purchasers. Based on these sample data, is it reasonable to conclude that one or more of these three age groups buys a disproportionate share of lottery tickets? Use a chi-square goodness-of-fit test with a
.05.

When public opinion surveys are conducted by mail, a cover letter explaining the purpose of the survey is usually included. To determine whether the wording of the cover letter influences the response rate, three different cover letters were used in a survey of students at a Midwestern university (The Effectiveness of Cover-Letter Appeals, Journal of Social Psychology [1984]: 8591). Suppose that each of the three cover letters accompanied questionnaires sent to an equal number of randomly selected students. Returned questionnaires were then classi- fied according to the type of cover letter (I, II, or III). Use the accompanying data to test the hypothesis that p1
1/3, p2
1/3, and p3
1/3, where p1, p2, and p3 are the true proportions of all returned questionnaires accompanied by cover letters I, II, and III, respectively. Use a .05 signifi- cance level. Cover-letter Type I II III Frequency 48 44 39

A certain genetic characteristic of a particular plant can appear in one of three forms (phenotypes). A researcher has developed a theory, according to which the hypothesized proportions are p1
.25, p2
.50, and p3
.25. A random sample of 200 plants yields X2
4.63. a. Carry out a test of the null hypothesis that the theory is correct, using level of significance a
.05. b. Suppose that a random sample of 300 plants had resulted in the same value of X2 . How would your analysis and conclusion differ from those in Part (a)?

The article Linkage Studies of the Tomato (Transactions of the Royal Canadian Institute [1931]: 119) reported the accompanying data on phenotypes resulting from crossing tall cut-leaf tomatoes with dwarf potato-leaf tomatoes. There are four possible phenotypes: (1) tall cut-leaf, (2) tall potato-leaf, (3) dwarf cut-leaf, and (4) dwarf potato-leaf. Phenotype 1 2 34 Frequency 926 288 293 104 Mendels laws of inheritance imply that p1
9/16, p2
3/16, p3
3/16, and p4
1/16. Are the data from this experiment consistent with Mendels laws? Use a .01 significance level.

It is hypothesized that when homing pigeons are disoriented in a certain manner, they will exhibit no preference for any direction of flight after takeoff. To test this, 120 pigeons are disoriented and released, and the direction of flight of each is recorded. The resulting data are given in the accompanying table. Direction Frequency 0 to 45 12 45 to 90 16 90 to 135 17 135 to 180 15 180 to 225 13 225 to 270 20 270 to 315 17 315 to 360 10 Use the goodness-of-fit test with significance level .10 to determine whether the data are consistent with this hypothesis. 12.1

A particular state university system has six campuses. On each campus, a random sample of students will be selected, and each student will be categorized with respect to political philosophy as liberal, moderate, or conservative. The null hypothesis of interest is that the proportion of students falling in these three categories is the same at all six campuses. a. On how many degrees of freedom will the resulting X2 test be based? b. How does your answer in Part (a) change if there are seven campuses rather than six? c. How does your answer in Part (a) change if there are four rather than three categories for political philosophy?

A random sample of 1000 registered voters in a certain county is selected, and each voter is categorized with respect to both educational level (four categories) and preferred candidate in an upcoming election for county supervisor (five possibilities). The hypothesis of interest is that educational level and preferred candidate are independent factors. a. If X2
7.2, what would you conclude at significance level .10? b. If there were only four candidates vying for election, what would you conclude if X2
14.5 and a
.05?

The polling organization Ipsos conducted telephone surveys in March of 2004, 2005, and 2006. In each year, 1001 people age 18 or older were asked about whether they planned to use a credit card to pay federal income taxes that year. The data given in the accompanying table are from the report Fees Keeping Taxpayers from Using Credit Cards to Make Tax Payments (IPSOS Insight, March 24, 2006). Is there evidence that the proportion falling in the three credit card response categories is not the same for all three years? Test the relevant hypotheses using a .05 significance level. Intent to Pay Taxes with a Credit Card 2004 2005 2006 Definitely/Probably Will 40 50 40 Might/Might Not/Probably Not 180 190 160 Definitely Will Not 781 761 801

In November 2005, an international study to assess public opinion on the treatment of suspected terrorists was conducted (Most in U.S., Britain, S. Korea and France Say Torture Is OK in at Least Rare Instances, Associated Press, December 7, 2005). Each individual in random samples of 1000 adults from each of nine different countries was asked the following question: Do you feel the use of torture against suspected terrorists to obtain information about terrorism activities is justified? Responses consistent with percentages given in the article for the samples from Italy, Spain, France, the United States, and South Korea are summarized in the accompanying table. Based on these data, is it reasonable to conclude that the response proportions are not the same for all five countries? Use a .01 significance level to test the appropriate hypotheses. Response Some- Not Country Never Rarely times Often Sure Italy 600 140 140 90 30 Spain 540 160 140 70 90 France 400 250 200 120 30 United States 360 230 270 110 30 South Korea 100 330 470 60 40

In a study to determine if hormone therapy increases risk of venous thrombosis in menopausal women, each person in a sample of 579 women who had been diagnosed with venous thrombosis was classified according to hormone use. Each woman in a sample of 2243 women who had not been diagnosed with venous thrombosis was also classified according to hormone use. Data from the study are given in the accompanying table (Journal of the American Medical Association [2004]: 1581 1587). The women in each of the two samples were selected at random from the patients at a large HMO in the state of Washington. a. Is there convincing evidence that the proportions falling in to each of the hormone use categories is not the same for women who have been diagnosed with venous thrombosis and those who have not? b. To what population would it be reasonable to generalize the conclusions of Part (a)? Explain. Current Hormone Use Conjugated Esterified Equine None Estrogen Estrogen Venous Thrombosis 372 86 121 No Venous Thrombosis 1439 515 289

The Harvard University Institute of Politics surveys undergraduates across the United States annually. Responses to the question When it comes to voting, do you consider yourself to be affiliated with the Democratic Party, the Republican Party, or are you Independent or unaffiliated with a major party? for the survey conducted in 2003, 2004, and 2005 are summarized in the given table. The samples for each year were independently selected and are considered to be representative of the population of undergraduate students in the year the survey was conducted. Is there evidence that the distribution of political affiliation is not the same for all three years for which data are given? Year Political Affiliation 2005 2004 2003 Democrat 397 409 325 Republican 301 349 373 Independent/unaffiliated 458 397 457 Other 60 48 48

The survey described in the previous exercise also asked the following question: Please tell me whether you trust the President to do the right thing all of the time, most of the time, some of the time, or never. Use the data in the given table and an appropriate hypothesis test to determine if there is evidence that trust in the President was not the same in 2005 as it was in 2002. Year Response 2005 2002 All of the time 132 180 Most of the time 337 528 Some of the time 554 396 Never 169 96

The report Undergraduate Students and Credit Cards in 2004 (Nellie Mae, May 2005) included information collected from individuals in a random sample of undergraduate students in the United States. Students were classified according to region of residence and whether or not they have one or more credit cards, resulting in the accompanying two-way table. Carry out a test to determine if there is evidence that region of residence and having a credit card are not independent. Use a
.05. Credit Card? At Least No One Credit Credit Region Card Cards Northeast 401 164 Midwest 162 36 South 408 115 West 104 23

The report described in the previous exercise also classified students according to region of residence and whether or not they had a credit card with a balance of more than $7000. Do these data support the conclusion that there is an association between region of residence and whether or not the student has a balance exceeding $7000? Test the relevant hypotheses using a .01 signifi- cance level. Balance Over $7000? Region No Yes Northeast 28 537 Midwest 162 182 South 42 481 West 9 118

The paper Overweight Among Low-Income Preschool Children Associated with the Consumption of Sweet Drinks (Pediatrics [2005]: 223229) described a study of children who were underweight or normal weight at age 2. Children in the sample were classified according to the number of sweet drinks consumed per day and whether or not the child was overweight one year after the study began. Is there evidence of an association between whether or not children are overweight after one hat it is reasonable to regard the sample of children in this study as representative of 2- to 3-year-old children and then test the appropriate hypotheses using a .05 significance level. Number of Sweet Overweight? Drinks Consumed per Day Yes No 0 22 930 1 73 2074 2 56 1681 3 or More 102 3390

Data consistent with summary quantities given in a paper that appeared in the British Medical Journal (Cigarette Tar Yields in Relation to Mortality from Lung Cancer in the Cancer Prevention Study II Prospective Cohort [2004]: 7279) are shown in the accompanying table. Suppose that the table was constructed by classifying individuals in a random sample of smokers according to gender and the age at which they began smoking. Do these data support the hypothesis that there is an association between gender and the age at which smoking began? Age When Gender Smoking Began Male Female 16 25 10 1617 24 17 1820 28 32 21 19 34

The 2006 Expedia Vacation Deprivation Survey (Ipsos Insight, May 18, 2006) described the results of a poll of working adults in Canada. Each person in a random sample was classified according to gender and the number of vacation days he or she usually took each year. The resulting data are summarized in the given table. Is it reasonable to conclude that there is an association between gender and the number of vacation days taken? To what population would it be reasonable to generalize this conclusion? Gender Days of Vacation Male Female None 51 42 15 21 25 610 67 79 1115 111 94 1620 71 70 2125 82 58 More than 25 118 79

The report Health Insurance Coverage of the Near Elderly (Urban Institute, July 2000) includes information from a study of American adults. The sample used in the study was a random sample of those who participated in the National Survey of Americas Families, a national survey of more than 100,000 people, and was considered to be representative of American adults. Using data consistent with summary quantities appearing in the report, the following table classifies individuals in the sample according to age group and whether or not the individual was considered to be in good health. Use the given data to test the hypothesis that age group and whether or not an individual is in good health are independent. Use a
.01. Health Status Good Poor Age Health Health 1834 920 80 3554 860 140 5564 790 210

A survey was conducted in the San Francisco Bay area in which each participating individual was classified according to the type of vehicle used most often and city of residence. A subset of the resulting data are given in the accompanying table (The Relationship of Vehicle Type Choice to Personality, Lifestyle, Attitudinal and Demographic Variables, Technical Report UCD-ITSRR02-06, DaimlerCrysler Corp., 2002).Vehicle Pleasant North San Type Concord Hills Francisco Small 68 83 221 Compact 63 68 106 Midsize 88 123 142 Large 24 18 11 Do the data provide convincing evidence of an association between city of residence and vehicle type? Use a significance level of .05. You may assume that it is reasonable to regard the sample as a random sample of Bay area residents.

Do women have different patterns of work behavior than men? The article Workaholism in Organizations: Gender Differences (Sex Roles: A Journal of Research [1999]: 333346) attempts to answer this question. Each person in a random sample of 423 graduates of a business school in Canada were polled and classified by gender and workaholism type, resulting in the accompanying table: Gender Workaholism Types Female Male Work Enthusiasts 20 41 Workaholics 32 37 Enthusiastic Workaholics 34 46 Unengaged Workers 43 52 Relaxed Workers 24 27 Disenchanted Workers 37 30 a. Test the hypothesis that gender and workaholism type are independent. b. The author writes women and men fell into each of the six workaholism types to a similar degree. Does the outcome of the test you performed in Part (a) support this conclusion? Explain.

The article Motion Sickness in Public Road Transport: The Effect of Driver, Route and Vehicle (Ergonomics [1999]: 16461664) reported that seat position within a bus may have some effect on whether one experiences motion sickness. The accompanying table classifies each person in a random sample of bus riders by the location of his or her seat and whether nausea was reported. Nausea No Nausea Front 58 870 Middle 166 1163 Rear 193 806 Based on these data, can you conclude that there is an association between seat location and nausea? Test the relevant hypotheses using a
.05

The article Mortality Among Recent Purchasers of Handguns (New England Journal of Medicine [1999]: 15831589) examined the relationship between handgun purchases and cause of death. Suppose that a random sample of 4000 death records was examined and cause of death was noted for each individual in the sample. Gun registration records were also examined to determine which of these 4000 individuals had purchased a handgun within the previous year. Data consistent with summary values given in the article are shown in the accompanying table. Not Suicide Suicide Handgun Purchased 4 12 No Handgun Purchased 63 3921 Is it reasonable to use the chi-square test to determine whether there is an association between handgun purchase within the year prior to death and whether the death was a suicide? Justify your answer.

A story describing a date rape was read by 352 high school students. To investigate the effect of the victims clothing on subjects judgment of the situation described, the story was accompanied by either a photograph of the victim dressed provocatively, a photo of the victim dressed conservatively, or no picture. Each student was asked whether the situation described in the story was one of rape. Data from the article The Influence of Victims Attire on Adolescent Judgments of Date Rape (Adolescence [1995]: 319323) are given in the accompanying table. Is there evidence that the proportion who believe that the story described a rape differs for the three different photo groups? Test the relevant hypotheses using a
.01. Picture No Response Provocative Conservative Picture Rape 80 104 92 Not Rape 47 12 17

Can people tell the difference between a female nose and a male nose? This important (?) research question was examined in the article You Can Tell by the Nose: Judging Sex from an Isolated Facial Feature (Perception [1995]: 969973). Eight Caucasian males and eight Caucasian females posed for nose photos. The article states that none of the volunteers wore nose studs or had prominent nasal hair. Each person placed a black Lycra tube over his or her head in such a way that only the nose protruded through a hole in the material. Photos were then taken from three different angles: front view, threequarter view, and profile. These photos were shown to a sample of undergraduate students. Each student in the sample was shown one of the nose photos and asked whether it was a photo of a male or a female; and the response was classified as either correct or incorrect. The accompanying table was constructed using summary values reported in the article. Is there evidence that the proportion of correct sex identifications differs for the three different nose views? View ThreeSex ID Front Profile Quarter Correct 23 26 29 Incorrect 17 14 11

The accompanying table appeared in the article Europes Receptivity to New Religious Movements: Round Two (Journal for the Scientific Study of Religion [1993]: 389397). Suppose that the percentages in the table were based on random samples of size 200 from each of the six countries. Percentage Who Believe in Country Fortune-Tellers Great Britain 42 West Germany 32 East Germany 22 Slovenia 55 Ireland 27 Northern Ireland 33 a. Use the given percentages to construct a two-way table with rows corresponding to the six countries and columns corresponding to the categories believe in fortune-tellers and dont believe in fortune-tellers. Enter the observed counts in the table. (Hint: The observed counts for Great Britain are (.42)(200)
84 for the believe column and (.58)(200)
116 for the dont believe column.) b. Is there evidence that the proportion who believe in fortune-tellers is not the same for all six countries? Test the relevant hypotheses using a
.01.

Job satisfaction of professionals was examined in the article Psychology of the Scientist: Work-Related Attitudes of U.S. Scientists (Psychological Reports [1991]: 443450). Each person in a random sample of 778 teachers was classified according to a job satisfaction variable and also by teaching level, resulting in the accompanying two-way table. Can we conclude that there is an association between job satisfaction and teaching level? Test the relevant hypotheses using a
.05. Job Satisfaction Teaching Level Satisfied Unsatisfied College 74 43 High School 224 171 Elementary 126 140

The article Victims Race Affects Killers Sentence, Study Finds (New York Times, April 20, 2001) included the following information:Defendants Victims Death Death Race Race Penalty Penalty Not white White 33 251 White White 33 508 Not white Not white 29 587 White Not white 4 76 The table was based on a study of all homicide cases in North Carolina for the period 1993 to 1997 where it was possible that the person convicted of murder could receive the death penalty. Explain why it would not be necessary (or appropriate) to use a chi-square test to determine if there was an association between the defendantvictim race combination and whether or not the convicted murderer receive a death sentence for convicted murders in North Carolina during 1993 to 1997.

Each member of the group should complete this step individually. Ask 25 different people to pick a digit from 0 to 9 at random. Record the responses.

Combine the responses you collected with those of the other members of your group to form a single sample. Summarize the resulting data in a one-way frequency table.

If people are adept at picking digits at random, what would you expect for the proportion of the responses in the sample that were 0? that were 1?

State a null hypothesis and an alternative hypothesis that could be tested to determine whether there is evidence that the 10 digits from 0 to 9 are not selected an equal proportion of the time when people are asked to pick a digit at random

Carry out the appropriate hypothesis test, and write a few sentences indicating whether or not the data support the theory that people are not good random number generators.

As a class, develop a plan for collecting the data. How will subjects be recruited? How will they be assigned to one of the two treatment groups (unaltered color, altered color)? What extraneous variables will be directly controlled, and how will you control them?

After the class is satisfied with the data collection plan, assign members of the class to prepare the gelatin to be used in the experiment.

Carry out the experiment, and summarize the resulting data in a two-way table like the one shown: Taste Rating Not Very Very Treatment Good Acceptable Good Unaltered Color Altered Color

The two-way table summarizes data from two independent samples (as long as subjects were assigned at random to the two treatments, the samples are independent). Carry out an appropriate test to determine whether the proportion for each of the three taste rating categories is the same when the color is altered as for when the color is not altered.

According to Census Bureau data, in 1998 the California population consisted of 50.7% whites, 6.6% blacks, 30.6% Hispanics, 10.8% Asians, and 1.3% other ethnic groups. Suppose that a random sample of 1000 students graduating from California colleges and universities in 1998 resulted in the accompanying data on ethnic group. These data are consistent with summary statistics contained in the article titled Crumbling Public School System a Threat to Californias Future (Investors Business Daily, November 12, 1999).Do the data provide evidence that the proportion of students graduating from colleges and universities in California for these ethnic group categories differs from the respective proportions in the population for California? Test the appropriate hypotheses using a
.01.

Criminologists have long debated whether there is a relationship between weather and violent crime. The author of the article Is There a Season for Homicide? (Criminology [1988]: 287296) classified 1361 homicides according to season, resulting in the accompanying data. Do these data support the theory that the homicide rate is not the same over the four seasons? Test the relevant hypotheses using a significance level of .05. Season Winter Spring Summer Fall 328 334 372 327

The following table is based on data reported in Light-to-Moderate Alcohol Consumption and Risk of Stroke Among U.S. Male Physicians (New England Journal of Medicine [1999]: 15571564). The table is based on 21,870 male physicians age 4084 who are participating in the Physicians Health Study. a. Calculate row percentages by dividing each observed count by the corresponding row total. Are the proportions falling in each of the alcohol consumption categories similar for the three smoking categories? b. Test the hypothesis that smoking status and alcohol consumption are independent. c. Is the result of your test in Part (b) consistent with what you expected based on your answer to Part (a)? If not, explain why your initial impression based on the percentages may not have been accurate. What aspect of the data set factors into your explanation?

Each boy in a sample of Mexican American males, age 1018, was classified according to smoking status and response to a question asking whether he likes to do risky things. The following table is based on data given in the article The Association Between Smoking and Unhealthy Behaviors Among a National Sample of Mexican-American Adolescents (Journal of School Health [1998]: 376379): Smoking Status Smoker Nonsmoker Likes Risky Things 45 46 Doesnt Like Risky Things 36 153 Assume that it is reasonable to regard the sample as a random sample of Mexican-American male adolescents. a. Is there sufficient evidence to conclude that there is an association between smoking status and desire to do risky things? Test the relevant hypotheses using a
.05. b. Based on your conclusion in Part (a), is it reasonable to conclude that smoking causes an increase in the desire to do risky things? Explain.

The article Cooperative Hunting in Lions: The Role of the Individual (Behavioral Ecology and Sociobiology [1992]: 445454) discusses the different roles taken by lionesses as they attack and capture prey. The authors were interested in the effect of the position in line as stalking occurs; an individual lioness may be in the center 682 C h a p t e r 12 The Analysis of Categorical Data and Goodness-of-Fit Tests Alcohol Consumption (No. of Drinks) a1/Wk 1/Wk 24/Wk 56/Wk 1/Day Never Smoked 3577 1711 2430 1211 1910 Smoked in the Past 1595 1068 1999 1264 2683 Currently Smokes 524 289 470 296 849of the line or on the wing (end of the line) as they advance toward their prey. In addition to position, the role of the lioness was also considered. A lioness could initiate a chase (be the first one to charge the prey), or she could participate and join the chase after it has been initiated. Data from the article are summarized in the accompanying table. Role Initiate Participate Position Chase in Chase Center 28 48 Wing 66 41 Is there evidence of an association between position and role? Test the relevant hypotheses using a
.01. What assumptions about how the data were collected must be true for the chi-square test to be an appropriate way to analyze these data?

The authors of the article A Survey of Parent Attitudes and Practices Regarding Underage Drinking (Journal of Youth and Adolescence [1995]: 315334) conducted a telephone survey of parents with preteen and teenage children. One of the questions asked was How effective do you think you are in talking to your children about drinking? Responses are summarized in the accompanying 3  2 table. Using a significance level of .05, carry out a test to determine whether there is an association between age of children and parental response. Age of Children Response Preteen Teen Very Effective 126 149 Somewhat Effective 44 41 Not at All Effective or Dont Know 51 26

The article Regional Differences in Attitudes Toward Corporal Punishment (Journal of Marriage and Family [1994]: 314324) presents data resulting from a random sample of 978 adults. Each individual in the sample was asked whether he or she agreed with the following statement: Sometimes it is necessary to discipline a child with a good, hard spanking. Respondents were also classified according to the region of the United States in which they lived. The resulting data are summarized in the accompanying table. Is there an association between response (agree, disagree) and region of residence? Use a
.01. Response Region Agree Disagree Northeast 130 59 West 146 42 Midwest 211 52 South 291 47

When charities solicit donations, they must know what approach will encourage people to donate. Would a picture of a needy child tug at the heartstrings and convince someone to contribute to the charity? As reported in the article The Effect of Photographs of the Handicapped on Donation (Journal of Applied Social Psychology [1979]: 426431), experimenters went door-to-door with four types of displays: a picture of a smiling child, a picture of an unsmiling child, a verbal message, and an identification of the charity only. At each door, they would randomly select which display to present. Suppose 18 of 30 subjects contributed when shown the picture of the smiling child, 14 of 30 contributed when shown the picture of an unsmiling child, 16 of 26 contributed when shown the verbal message, and 18 of 22 contributed when shown only the identification of the charity. What conclusions can be drawn from these data? Explain your procedure and reasoning.

Jail inmates can be classified into one of the following four categories according to the type of crime committed: violent crime, crime against property, drug offenses, and public-order offenses. Suppose that random samples of 500 male inmates and 500 female inmates are selected, and each inmate is classified according to type of offense. The data in the accompanying table are based on summary values given in the article Profile of Jail Inmates (USA Today, April 25, 1991). We would like to know whether male and female inmates differ with respect to type of offense.Type of Crime Male Female Violent 117 66 Property 150 160 Drug 109 168 Public-Order 124 106 a. Is this a test of homogeneity or a test of independence? b. Test the relevant hypotheses using a significance level of .05.

Drivers born under the astrological sign of Capricorn are the worst drivers in Australia, according to an article that appeared in the Australian newspaper The Mercury (October 26, 1998). This statement was based on a study of insurance claims that resulted in the following data for male policyholders of a large insurance company. Astrological Number of Sign Policyholders Aquarius 35,666 Aries 37,926 Cancer 38,126 Capricorn 54,906 Gemini 37,179 Leo 37,354 Libra 37,910 Pisces 36,677 Sagittarius 34,175 Scorpio 35,352 Taurus 37,179 Virgo 37,718 a. Assuming that it is reasonable to treat the policyholders of this particular insurance company as a random sample of insured drivers in Australia, are the observed data consistent with the hypothesis that the proportion of policyholders is the same for each of the 12 astrological signs? b. Why do you think that the proportion of Capricorn policyholders is so much higher than would be expected if the proportions are the same for all astrological signs? c. Suppose that a random sample of 1000 accident claims submitted to this insurance company is selected and each claim classified according to the astrological sign of the driver. (The accompanying table is consistent with accident rates given in the article.) Astrological Observed Number Sign in Sample Aquarius 85 Aries 83 Cancer 82 Capricorn 88 Gemini 83 Leo 83 Libra 83 Pisces 82 Sagittarius 81 Scorpio 85 Taurus 84 Virgo 81 Test the null hypothesis that the proportion of accident claims submitted by drivers of each astrological sign is consistent with the proportion of policyholders of each sign. Use the information on the distribution of policyholders from Part (a) to compute expected frequencies and then carry out an appropriate test.

The article Identification of Cola Beverages (Journal of Applied Psychology [1962]: 356360) reported on an experiment in which each of 79 subjects was presented with glasses of cola in pairs and asked to identify which glass contained a specific brand of cola. The accompanying data appeared in the article. Do these data suggest that individuals abilities to make correct identifi- cation differ for the different brands of cola? Number of Correct Identifications Cola 0 1 2 3 or 4 Coca-Cola 13 23 24 19 Pepsi Cola 12 20 26 21 Royal Crown 18 28 19 14