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nonparasitized fish? Test using « = .01. the late-game leader was determined, and then it
——— was noted whether the late-game leader actually
Treatment —_Parasitized _Nonparasitized ended up winning the game. The resulting data is
—— 90 3 summarized in the accompanying table.
ee e ‘ 6 Late-Game —_Late-Game
Sport Leader Wins Leader Loses
38. Qualifications of male and female head and Basketball 150 39
assistant college athletic coaches were compared Baseball 86 6
in the article “Sex Bias and the Validity of Hockey 65 15
Believed Differences Between Male and Female Football 72 21
Interscholastic Athletic Coaches” (Res. Q. Exer- ——ewsw>s—wma
cise Sport, 1990: 259-267). Each person in ran- The authors state, “Late-game leader is defined
dom samples of 2225 male coaches and 1141 as the team that is ahead after three quarters in
female coaches was classified according to num- basketball and football, two periods in hockey,
ber of years of coaching experience to obtain the and seven innings in baseball. The chi-square
accompanying two-way table. Is there enough
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13.3 Supplementary Exercises 755
value on three degrees of freedom is 10.52 from each of three different areas near industrial
(P < .015).” facilities. Each individual was asked whether he
a. State the relevant hypotheses and reach a or she noticed odors (1) every day, (2) at least
conclusion using % = .05. once/week, (3) at least once/month, (4) less often
b. Do you think that your conclusion in part (a) than once/month, or (5) not at all, resulting in the
can be attributed to a single sport being an output from SPSS on the next page. State and test
anomaly? the appropriate hypotheses.
40. The accompanying two-way frequency table 43. Many shoppers have expressed unhappiness
appears in the article “Marijuana Use in because grocery stores have stopped putting
College” (Youth and Society, 1979: 323-334). prices on individual grocery items. The article
Each of 445 college students was classified “The Impact of Item Price Removal on Grocery
according to both frequency of marijuana Shopping Behavior” (J. Market., 1980: 73-93)
use and parental use of alcohol and psychoactive reports on a study in which each shopper in a
drugs. Does the data suggest that parental usage sample was classified by age and by whether he
and student usage are independent in or she felt the need for item pricing. Based on the
the population from which the sample was accompanying data, does the need for item pric-
drawn? Use the P-value method to reach a con- ing appear to be independent of age?
clusion. _———————— ee
Age
Standard Level of ———
Marijuana use < 30 30-39 40-49 50-59 > 60
Never Occasional Regular —— re ee
. Number 150 141 82 63 49
Parental Neither fa | | 40 in Sample
Useot One | os | a | 51 Number 127 118 77 61 41
Alcohol Who Want
and Drugs Roth 7 nN 19 Item Pricing
41. Ina study of 2989 cancer deaths, the location of _ 44 Let p; denote the proportion of successes in a
death (home, acute-care hospital, or chronic-care particular population. The test statistic value in
facility) and age at death were recorded, resulting Chapter 9 for testing Ho: pi = pio was 2 =
in the given two-way frequency table (“Where (P1 —pio)/V/Piopm/n, where px =1 — pro.
Cancer Patients Die,” Public Health Rep., 1983: Show that for the case k = 2, the chi-squared sta-
173). Using a .01 significance level, test the null tistic value of Section 13.1 satisfies 7? = 2°. [Hinr:
hypothesis that age at death and location of death First show that (71) — pio)” = (2 —np20)"-]
are independent, 45. The NCAA basketball tournament begins with 64
tion teams that are apportioned into four regional tour-
ocation : A
naments, each involving 16 teams. The 16 teams
Age Home Acute-Care Chronic-Care in each region are then ranked (seeded) from | to
a 16. During the 12-year period from 1991 to 2002,
15-54 94 418 23 the top-ranked team won its regional tournament
55-64 116 524 34 22 times, the second-ranked team won 10 times,
65-74 156 581 109 the third-ranked team won 5 times, and the
Over 74 138 558 238 remaining 11 regional tournaments were won
— by teams ranked lower than 3, Let P,, denote
42. In a study to investigate the extent to which the probability that the team ranked i in its region
individuals are aware of industrial odors in a is victorious in its game against the team ranked
certain region (“Annoyance and Health Reac- Jj. Once the Pj’s are available, it is possible to
tions to Odor from Refineries and Other Indus- compute the probability that any particular seed
tries in Carson, California,” Environ. Res., 1978: wins its regional tournament (a complicated
119-132), a sample of individuals was obtained calculation because the number of outcomes
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756 charter 13 Goodness-of-Fit Tests and Categorical Data Analysis
Trosstabulation: AREA By CATEGORY
Count
Exp val
CATEGORY Row Pct Row
AREA Col Pct 1.00 2.00 3.00 4.00 5.00 Total
1.00 20 28 23 14 12 97
Tat 24.7 18.0 16.0 25.7 33.3%
20.6% 28.9% 23.7% 14.4% 12.4%
52.6% | 37.8% | 42.6% | 29.28 | 15.6%
2.00 14 34 21 14 12 95
12.4 24.2 17.6 15.7 25.1 32.6%
14.7% 35.8% 22.1% 14.7% 12.6%
36.8% 45.9% 38.9% 29.2% 15.6%
3.00 4 12 10 20 53 99
12.9 25.2 18.4 16.3 26.2 34.0%