8.84 Oil spill impact on seabirds. Refer to the Journal of Agricultural, Biological, and Environmental Statistics (Sept. 2000) study of the impact of a tanker oil spill on the seabird population in Alaska, presented in Exercise 2.201 (p. 109). Recall that for each of 96 shoreline locations (called transects), the number of seabirds found, the length (in kilometers) of the transect, and whether or not the transect was in an oiled area were recorded. (The data are saved in the EVOS file.) Observed seabird density is defined as the observed count divided by the length of the transect. A comparison of the mean densities of oiled and unoiled transects is displayed in the MINITAB printout below. Use this information to make an inference about the difference in the population mean seabird densities of oiled and unoiled transects.

MINITAB Output for Exercise 8.84

HYBRID 8.85 Safety of hybrid cars. According to the Highway Loss Data Institute (HLDI), “hybrid [automobiles] have a safety edge over their conventional twins when it comes to shielding their occupants from injuries in crashes” (HLDI Bulletin, Sept. 2011). Consider data collected by the HLDI on Honda Accords over the past eight years. In a sample of 50,132 collision claims for conventional Accords, 5,364 involved injuries; in a sample of 1,505 collision claims for hybrid Accords, 137 involved injuries. You want to use this information to determine whether the injury rate for hybrid Accords is less than the injury rate for conventional Accords.

1. Identify the two qualitative variables measured for each Honda Accord collision claim.

2. Form a contingency table for this data, giving the number of claims in each combination of the qualitative variable categories.

3. Give H₀ and H_a for testing whether injury rate for collision claims depends on Accord model (hybrid or conventional).

4. Find the expected number of claims in each cell of the contingency table, assuming that H₀ is true.

5. Compute the ${\chi }^2$ test statistic and compare your answer to the test statistic shown on the SAS printout on p. 489.

6. Find the rejection region for the test using $\alpha =.05$ and compare your answer to the critical value shown on the accompanying SAS printout.

7. Make the appropriate conclusion using both the rejection region method and the p-value (shown on the SAS printout).

8. Find a 95% confidence interval for the difference between the injury rates of conventional and hybrid Honda Accords. Use the interval to infer whether the injury rate for hybrid Accords is less than the injury rate for conventional Accords.

SAS Output for Exercise 8.85

POTTERY 8.86 Excavating ancient pottery. Refer to the Chance (Fall 2000) study of ancient Greek pottery, presented in Exercise 2.186 (p. 106). Recall that 837 pottery pieces were uncovered at the excavation site. The table describing the types of pottery found is reproduced here.

1. Describe the qualitative variable of interest in the study. Give the levels (categories) associated with the variable.

2. Assume that the four types of pottery occur with equal probability at the excavation site. What are the values of $p_1,p_2,p_3,$ and $p_4,$ the probabilities associated with the four pottery types?

3. Give the null and alternative hypotheses for testing whether one type of pottery is more likely to occur at the site than any of the other types.

4. Find the test statistic for testing the hypotheses stated in part c.

5. Find and interpret the p-value of the test. State the conclusion in the words of the problem if you use $\alpha =.10.$

8.87 Racial profiling by the LAPD. Racial profiling is a term used to describe any police action that relies on ethnicity rather than behavior to target suspects engaged in criminal activities. Does the Los Angeles Police Department (LAPD) invoke racial profiling in stops and searches of Los Angeles drivers? This question was addressed in Chance (Spring 2006).

1. Data on stops and searches of both African-Americans and white drivers over a six-month period are summarized in the accompanying table. Conduct a test (at $\alpha =.05$) to determine whether there is a disparity in the proportions of African-American and white drivers who are searched by the LAPD after being stopped.

   

2. The LAPD defines a “hit rate” as the proportion of searches that result in a discovery of criminal activity. Use the data in the table to estimate the disparity in the hit rates for African-American and white drivers under a 95% confidence interval. Interpret the results.

8.88 The “winner’s curse” in auction bidding. In auction bidding, the “winner’s curse” is the phenomenon of the winning (or highest) bid price being above the expected value of the item being auctioned. The Review of Economics and Statistics (Aug. 2001) published a study on whether experience in bidding affects the likelihood of the winner’s curse occurring. Two groups of bidders in a sealed-bid auction were compared: (1) superexperienced bidders and (2) less experienced bidders. In the superexperienced group, 29 of 189 winning bids were above the item’s expected value; in the less experienced group, 32 of 149 winning bids were above the item’s expected value.

1. Find an estimate of $p_1,$ the true proportion of super-experienced bidders who fall prey to the winner’s curse.

2. Find an estimate of $p_2,$ the true proportion of less experienced bidders who fall prey to the winner’s curse.

3. Construct a 90% confidence interval for $p_1- p_2.$

4. Give a practical interpretation of the confidence interval you constructed in part c. Make a statement about whether experience in bidding affects the likelihood of the winner’s curse occurring.

ETHNIC 8.89 Politics and religion. University of Maryland professor Ted R. Gurr examined the political strategies used by ethnic groups worldwide in their fight for minority rights (Political Science & Politics, June 2000). Each in a sample of 275 ethnic groups was classified according to world region and highest level of political action reported. The data are summarized in the contingency table above. Conduct a test at $\alpha =.10$ to determine whether political strategy of ethnic groups depends on world region. Support your answer with a graph.

Table for Exercise 8.89

Alternate View

		Political Strategy
		No Political Action	Mobilization, Mass Action	Terrorism, Rebellion, Civil War
World Region	Latin American	24	31	7
	Post-Communist	32	23	4
	South, Southeast, East Asia	11	22	26
	Africa/Middle East	39	36	20

FLDWRK 8.90 Sociology fieldwork methods. Refer to the Teaching Sociology (July 2006) study of the fieldwork methods used by qualitative sociologists, presented in Exercise 2.193 (p. 108). Recall that fieldwork methods can be categorized as follows: Interview, Observation plus Participation, Observation Only, and Grounded Theory. The table in the next column shows the number of papers published over the past seven years in each category. Suppose a sociologist claims that 70%, 15%, 10%, and 5% of the fieldwork methods involve interview, observation plus participation, observation only, and grounded theory, respectively. Do the data support or refute the claim? Explain.

COLDRK 8.91 The Family and Consumer Sciences Research Journal (Mar. 2005) published a study of college students and drinking. One of the researchers’ main objectives was to segment college students according to their rates of alcohol consumption. A segmentation was developed based on survey responses to the questions on frequency of drinking and average number of drinks per occasion for a sample of 657 students. Four types, or groups, of college drinkers emerged: non/seldom drinkers, social drinkers, typical binge drinkers, and heavy binge drinkers. Frequencies are shown in the accompanying SPSS printout. Is this sufficient evidence to indicate that the true proportions in the population of college students are different?

COLDRK 8.92 Refer to the Family and Consumer Sciences Research Journal (Mar. 2005) study of college students and drinking, Exercise 8.91 . A second objective of the researchers was to establish a statistical link between the frequency of drinking (none, once per month, twice per week, or more) and the amount of alcohol consumed (none, 1 drink, 2–3 drinks, 4–6 drinks, 7–9 drinks, or more). That is, the researchers sought a link between frequency of drinking alcohol over the previous one-month period and average number of drinks consumed per occasion.

An SPSS contingency table analysis relating frequency of drinking to average amount of alcohol consumed is shown on p. 491.

These results led the researchers to report that “The frequent drinkers were more likely to consume more [alcohol] on each occasion, a tendency that clearly makes them heavy drinkers.” Do you agree? Explain.

SOUVNR 8.93 Purchasing souvenirs. A major tourist activity is shopping. Travel researchers estimate that nearly one-third of total travel expenditures are used on shopping for souvenirs (Journal of Travel Research, May 2011). To investigate the impact of gender on souvenir shopping, a survey of 3,200 tourists was conducted. One question asked how often the tourist purchases photographs, postcards, or paintings of the region visited. Responses were recorded as “always,” “often,” “occasionally,” or “rarely or never.” The next table shows the percentages of tourists responding in each category by gender.

SPSS output for Exercise 8.92

1. Based on the percentages shown in the table, do you think male and female tourists differ in their responses to purchasing photographs, postcards, or paintings? Why are these percentages alone insufficient to draw a conclusion about the true response category proportions?

2. Assume that 1,500 males and 1,700 females participated in the survey. Use these sample sizes and the percentages in the table to compute the counts of tourists in each of the Response/Gender categories. This represents the contingency table for the study.

3. Specify the null and alternative hypotheses for testing whether male and female tourists differ in their responses to purchasing photographs, postcards, or paintings.

4. An SPSS printout of the contingency table analyses is shown in the next column. Locate the test statistic and p-value on the printout.

5. Make the appropriate conclusion using $\alpha =.01$.

8.94 Killing insects with low oxygen. Refer to the Journal of Agricultural, Biological, and Environmental Statistics (Sept. 2000) study of the mortality of rice weevils exposed to low oxygen, presented in Exercise 6.92 (p. 346). Recall that 31,386 of 31,421 rice weevils were found dead after exposure to nitrogen gas for 4 days. In a second experiment, 23,516 of 23,676 rice weevils were found dead after exposure to nitrogen gas for 3.5 days. Conduct a test of hypothesis to compare the mortality rates of adult rice weevils exposed to nitrogen at the two exposure times. Is there a significant difference (at $\alpha =.10$) in the mortality rates?

8.95 Effectiveness of drug tests of Olympic athletes. Erythropoietin (EPO) is a banned drug used by athletes to increase the oxygen-carrying capacity of their blood. New tests for EPO were first introduced prior to the 2000 Olympic Games held in Sydney, Australia. Chance (Spring 2004) reported that of a sample of 830 world-class athletes, 159 did not compete in the World Championships (a year prior to the introduction of the new EPO test). Similarly, 133 of 825 potential athletes did not compete in the 2000 Olympic games. Was the new test effective in deterring an athlete from participating in the Olympics? Conduct the analysis (at $\alpha =.10$) and draw the proper conclusion.

HRM 8.96 Masculinity and crime. Refer to the Journal of Sociology (July 2003) study on the link between the level of masculinity and criminal behavior in men, presented in Exercise 7.25 (p. 386). The researcher identified events that a sample of newly incarcerated men were involved in and classified each event as “violent” (involving the use of a weapon, the throwing of objects, punching, choking, or kicking) or “avoided-­violent” (involving pushing, shoving, grabbing, or threats of violence that did not escalate into a violent event). Each man (and corresponding event) was also classified as possessing “high-risk masculinity” (scored high on the Masculinity–Femininity Scale test and low on the Traditional Outlets of Masculinity Scale test) or “low-risk masculinity.” The data on 1,507 events are summarized in the following table.

1. Identify the two categorical variables measured (and their levels) in the study.

2. Identify the experimental units.

3. If the type of event (violent or avoided-violent) is independent of high-/low-risk masculinity, how many of the 1,507 events would you expect to be violent and involve a high-risk-masculine man?

4. Repeat part c for the other combinations of event type and high-/low-risk masculinity.

5. Calculate the ${\chi }^2$ statistic for testing whether event type depends on high- low-risk masculinity.

6. Give the appropriate conclusion of the test mentioned in part e, using $\alpha =.05.$

8.97 Multiple sclerosis drug. Interferons are proteins produced naturally by the human body that help fight infections and regulate the immune system. A drug developed from interferons, called Avonex, is now available for treating patients with multiple sclerosis (MS). In a clinical study, 85 MS patients received weekly injections of Avonex over a two-year period. The number of exacerbations (i.e., flare-ups of symptoms) was recorded for each patient and is summarized in the accompanying table. For MS patients who take a placebo (no drug) over a similar two-year period, it is known from previous studies that 26% will experience no exacerbations, 30% one exacerbation, 11% two exacerbations, 14% three exacerbations, and 19% four or more exacerbations.

1. Conduct a test to determine whether the exacerbation distribution of MS patients who take Avonex differs from the percentages reported for placebo patients. Use $\alpha =.05.$

2. Find a 95% confidence interval for the true percentage of Avonex MS patients who remain free of exacerbations during a two-year period.

3. Refer to part b. Is there evidence that Avonex patients are more likely to have no exacerbations than placebo patients? Explain.

GEESE 8.98 Flight response of geese to helicopter traffic. Offshore oil drilling near an Alaskan estuary has led to increased air traffic—mostly large helicopters—in the area. The U.S. Fish and Wildlife Service commissioned a study to investigate the impact these helicopters have on the flocks of Pacific brant geese that inhabit the estuary in the fall before migrating (Statistical Case Studies: A Collaboration between Academe and Industry, 1998). Two large helicopters were flown repeatedly over the estuary at different altitudes and lateral distances from the flock. The flight responses of the geese (recorded as “low” or “high”), the altitude (in hundreds of meters), and the lateral distance (also in hundreds of meters) for each of 464 helicopter overflights were recorded and are saved in the GEESE file. The data for the first 10 overflights are shown in the following table.

1. The researchers categorized altitude as follows: less than 300 meters, 300–600 meters, and 600 or more meters. Summarize the data by creating a contingency table for altitude category and flight response.

2. Conduct a test to determine whether flight response of the geese depends on altitude of the helicopter. Test, using $\alpha =.01.$

3. The researchers categorized lateral distance as follows: less than 1,000 meters, 1,000–2,000 meters, 2,000–3,000 meters, and 3,000 or more meters. Summarize the data in the GEESE file by creating a contingency table for lateral distance category and flight response.

4. Conduct a test to determine whether flight response of the geese depends on lateral distance of helicopter from the flock. Test, using $\alpha =.01.$

5. The current Federal Aviation Authority (FAA) mini­mum altitude standard for flying over the estuary is 2,000 feet (approximately 610 meters). On the basis of the results obtained in parts a–d, what changes to the FAA regulations do you recommend in order to minimize the effects to Pacific brant geese?

TRENCH 8.99 Defensible landscapes in archaeology. The defensibility of a given landscape in the Northwest United States was studied in the Journal of Anthropological Archaeology (May 2014). Archaeologists typically define “defensive” locations as those that are hidden with high elevation and escape routes. A question arose regarding the defensibility of trench embankments. Each in a sample of 1,914 archaeological sites was classified as “highly defensible” or not. In addition, whether the site was located in a trench embankment was determined. The results of the categorizations (number of sites in each category) are summarized below.

Alternate View

	Highly Defensible	Not Highly Defensible	Total
Trench Embankment	9	14	23
Non-trench Embankment	311	1,580	1,891

1. Is this sufficient evidence to conclude that the proportion of trench embankment sites that are “highly defensible” differs from the corresponding proportion of non-trench embankment sites? That is, is the defensibility status of a site dependent on site type (trench embankment or not)?

2. Fisher’s exact test (see Exercise 13.45 ) resulted in a p-value of $p=.008$. Interpret this result, and then explain why this test is preferred over the ${\chi }^2$ test in part a.

MDIQ 8.100 IQ and mental deficiency. A person is diagnosed with a mental deficiency if, before the age of 18, his/her score on a standard IQ test is no higher than 70 (two standard deviations below the mean of 100). Researchers at Cornell and West Virginia Universities examined the impact of rising IQ scores on diagnoses of mental deficiency (MD) (American Psychologist, Oct. 2003). IQ data were collected from different school districts across the United States, and the students were tested with either the Wechsler Intelligence Scale for Children—Revised (WISC-R) or the Wechsler Intelligence Scale for Children—Third Revision (WISC-III) IQ tests. The researchers focused on those students with IQs just above the mental deficiency cutoff (between 70 and 85), based on the original IQ test. These “borderline” MD students were then retested one year later with one of the IQ tests. The accompanying table gives the number of students diagnosed with mental deficiency on the basis of the retest. Conduct a chi-square test for independence to determine whether the proportion of students diagnosed with MD depends on the IQ test/retest method. Use $\alpha =.01.$

Table for Exercise 8.101

HYPNOS 8.101 Susceptibility to hypnosis. A standardized procedure for determining a person’s susceptibility to hypnosis is the Stanford Hypnotic Susceptibility Scale, Form C (SHSS:C). Recently, a new method called the Computer-Assisted Hypnosis Scale (CAHS), which uses a computer as a facilitator of hypnosis, has been developed. Each scale classifies a person’s hypnotic susceptibility as low, medium, high, or very high. Researchers at the University of Tennessee compared the two scales by administering both tests to each of 130 undergraduate volunteers (Psychological Assessment, Mar. 1995). The hypnotic classifications are summarized in the table at the bottom of the page. A contingency table analysis will be performed to determine whether CAHS level and SHSS level are independent.

1. Check to see if the assumption of expected cell counts of 5 or more is satisfied. Should you proceed with the analysis? Explain.

2. One way to satisfy the assumption of part a is to combine the data for two or more categories (e.g., high and very high) in the contingency table. Form a new contingency table by combining the data for the high and very high categories in both the rows and the columns.

3. Calculate the expected cell counts in the new contingency table you formed in part c. Is the assumption now satisfied?

4. Perform the chi-square test on the new contingency table. Use $\alpha =.05.$ Interpret the results.

SEED 8.102 Subarctic plant study. The traits of seed-bearing plants indigenous to subarctic Finland were studied in Arctic, Antarctic, and Alpine Research (May 2004). Plants were categorized according to type (dwarf shrub, herb, or grass), abundance of seedlings (no seedlings, rare seedlings, or abundant seedlings), regenerative group (no vege­tative reproduction, vegetative reproduction possible, vegetative reproduction ineffective, or vegetative reproduction effective), seed weight class (0–.1, .1–.5, .5–1.0, 1.0–5.0, and $>5.0\mathrm{m}\mathrm{i}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{s}$), and diaspore morphology (no structure, pappus, wings, fleshy fruits, or awns/hooks). The data on a sample of 73 plants are saved in the SEED file.

1. A contingency table for plant type and seedling abundance, produced by MINITAB, is shown here. (Note: $\mathrm{N}\mathrm{S}=\mathrm{n}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{e}\mathrm{d}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{s},\mathrm{S}\mathrm{A}=\mathrm{s}\mathrm{e}\mathrm{e}\mathrm{d}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{s}$ abundant, and $\mathrm{S}\mathrm{R}=\mathrm{s}\mathrm{e}\mathrm{e}\mathrm{d}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{s}$ rare.) Suppose you want to perform a chi-square test of independence to determine whether seedling abundance depends on plant type. Find the expected cell counts for the contingency table. Are the assumptions required for the test satisfied?

   

2. Reformulate the contingency table by combining the NS and SR categories of seedling abundance. Find the expected cell counts for this new contingency table. Are the assumptions required for the test satisfied?

3. Reformulate the contingency table of part b by combining the dwarf shrub and grasses categories of plant type. Find the expected cell counts for this contingency table. Are the assumptions required for the test satisfied?

4. Carry out the chi-square test for independence on the contingency table you came up with in part c, using $\alpha =.10.$ What do you conclude?

GUILT 8.103 Guilt in decision making. The effect of guilt emotion on how a decision maker focuses on the problem was investigated in the Jan. 2007 issue of the Journal of Behavioral Decision Making. A total of 171 volunteer students participated in the experiment, where each was randomly assigned to one of three emotional states (guilt, anger, or neutral) through a reading/writing task. Immediately after the task, the students were presented with a decision problem where the stated option has predominantly negative features (e.g., spending money on repairing a very old car). The results (number responding in each category) are summarized in the accompanying table. Is there sufficient evidence (at $\alpha =.10$) to claim that the option choice depends on emotional state?

8.104 Gambling in public high schools. With the rapid growth in legalized gambling in the United States, there is concern that the involvement of youth in gambling activities is also increasing. University of Minnesota professor Randy Stinchfield compared the annual rates of gambling among Minnesota public school students (Journal of Gambling Studies, Winter 2001). Based on survey data, the following table shows the percentages of ninth-grade boys who gambled weekly or daily on any game (e.g., cards, sports betting, lotteries) for two years:

1. Are the percentages of ninth-grade boys who gambled weekly or daily on any game in the two years significantly different? (Use $\alpha =.01.$)

2. Professor Stinchfield states that “because of the large sample sizes, even small differences may achieve statistical significance, so interpretations of the differences should include a judgment regarding the magnitude of the difference and its public health significance.” Do you agree with this statement? If not, why not? If so, obtain a measure of the magnitude of the difference between the two years and attach a measure of reliability to the difference.

8.105 Goodness-of-fit test. A statistical analysis is to be done on a set of data consisting of 1,000 monthly salaries. The analysis requires the assumption that the sample was drawn from a normal distribution. A preliminary test, called the ${\chi }^2$ goodness-of-fit test, can be used to help determine whether it is reasonable to assume that the sample is from a normal distribution. Suppose the mean and standard deviation of the 1,000 salaries are hypothesized to be $1,200 and $200, respectively. Using the standard normal table, we can approximate the probability of a salary being in the intervals listed in the table in the next column. The third column represents the expected number of the 1,000 salaries to be found in each interval if the sample was drawn from a normal distribution with $\mu =\$1,200$ and $\sigma =\$200$. Suppose the last column contains the actual observed frequencies in the sample. Large differences between the observed and expected frequencies cast doubt on the normality assumption.

Table for Exercise 8.106

Alternate View

Interval	Probability	Expected Frequency	Observed Frequency
Less than $800	.023	23	26
$\$8000<\$1,000$	.136	136	146
$\$\mathrm{1,000}<\$1,200$	.341	341	361
$\$1,200<\$1,400$	.341	341	311
$\$1,400<\$1,600$	.136	136	143
$1,600 or above	.023	23	13

1. Compute the ${\chi }^2$ statistic on the basis of the observed and expected frequencies.

2. Find the tabulated ${\chi }^2$ value when $\alpha =.05$ and there are five degrees of freedom. (There are $k- 1=5$ df associated with this ${\chi }^2$ statistic.)

3. On the basis of the ${\chi }^2$ statistic and the tabulated ${\chi }^2$ value, is there evidence that the salary distribution is nonnormal?

4. Find the approximate observed significance level for the test in part c.

8.106 Testing normality. Suppose a random variable is hypothesized to be normally distributed with a mean of 0 and a standard deviation of 1. A random sample of 200 observations of the variable yields frequencies in the intervals listed in the table shown above. Do the data provide sufficient evidence to contradict the hypothesis that x is normally distributed with $\mu =0$ and $\sigma =1?$ Use the technique developed in Exercise 8.105 .