- Applications
Chi-square Test Application Questions
Random Jury Pool?
A defense attorney claimed that a jury pool is not representative of the larger population in the court’s district. In particular, she was concerned that the jury pool contained fewer “young people” than would be expected based on district demographics. To test her claim, she created seven age categories, counted the number of individuals from the jury pool in each age category, and found the percentage of the district in each age category from the most recent census data. Her findings are below.
Ages 18-19 20-24 25-29 30-39 40-49 50-64 65+ Jury Pool 23 96 134 293 297 380 113 District 6.1% 15.0% 13.5% 21.7% 15.3% 18.2% 10.2%
Use these results to determine, at the 10% level, if the age distribution in the jury pool accurately represents the age distriction of the district as a whole. Also comment on whether the attorney’s specific concern was warranted.
Shrike Habitat Use
In the same study used in the example of this module, Bohall and Wood (1987) more closely examined the habitat use of the shrikes observed in the open habitat by looking at four “sub-habitats” within these areas. Of the 1456 shrike observations in this habitat, 149 were in “settled” areas, 944 were in improved pastures, 192 were in overgrown pastures, and 171 were in crop fields. In addition, 20.5% of this habitat was considered to be “settled”, 58.6% was improved pasture, 10.3% was overgrown pasture, and 10.6% was crop fields. Use these results to determine, at the 5% level, if shrikes found in open areas use the sub-habitats in proportion to their availability.
Media Treatment of President Clinton
Between June 11 and 15, 1993, the Times Mirror Center for People and the Press interviewed 1006 adults concerning their views on media treatment of the then newly inaugurated President Clinton. They found 433 of those sampled felt that news organizations were “criticizing Clinton unfairly.” Test the hypothesis (with α = 0.10) that more than 45% of all adults feel that Clinton has been criticized unfairly.
Corn Genetics
A particular type of corn is known to have one of four types of kernels: purple-smooth, purple-wrinkled, yellow-smooth, and yellow-wrinkled (see figure below). The purple (P) and smooth (S) alleles are dominant. The cross between heterozygous individuals (i.e., PpSs) should produce a 9:3:3:1 ratio of purple-smooth, purple-wrinkled, yellow-smooth, and yellow-wrinkled individuals. Of the kernels shown in the graphic to the right (a random picture location but not a random selection of each individual) 32 are purple-smooth, 14 are purple-wrinkled, 8 are yellow-smooth, and 4 are yellow-wrinkled. Use the results to determine, at the 5% level, if the theoretical 9:3:3:1 ratio is upheld with these data.
Lake Association Survey
The leader of a local lake association conducted a survey of all members of the association. One question on the survey was, “What is your preferred method of receiving notices from the lake association: by regular mail, by e-mail, by phone, by poster (at the local boat landing), or other?” Of the surveys returned, 47 respondents preferred regular mail, 63 e-mail, 17 phone, 73 by poster, and 8 some other method. Of the respondents who did not prefer some other method, is there evidence, at the 5% level, of a difference in the preferred method of contact?
Fair Coin?
While imprisoned by the Germans during World War II, the English mathematician John Kerrich tossed a coin 10000 times and obtained 5067 heads. Use his results to determine (at the 1% level) whether the coin was fair or not (i.e., equal chance of heads and tails).
Distribution of Blood Types
Past data suggest that of the patients that a hospital serves 44% have type O, 45% have type A, 8% have type B, and 3% have type AB blood. In a more recent survey they found that 67 patients had type O, 83 had type A, 29 had type B, and 8 had type AB. Use the more recent results to determine, at the 5% level, if the past results still hold.
Poll of Political Support
A county district attorney would like to run for the office of state district attorney. She has decided that she will give up her county office and run for state office if more than 65% of her party constituents support her. As her campaign manager, you collected data on 950 randomly selected party members and find that 660 party members support the candidate. Test at the 5% significance level whether she should give up her county office and run for the state office.
Age Distribution of Deer
Suppose that you know that a population of deer is at a stable age distribution and stable population size. In addition, it is hypothesized that the survival rate from year-to-year is 50%. Through a random sample of animals from this population you determine that 134 are in the 0-1 age group, 66 are aged 1-2, 30 are aged 2-3, 13 are aged 3-4, 4 are aged 4-5, and 6 are aged 5-6. Use these results to determine, at the 10% level, if the survival rate is indeed 50%. [Hint: Find the expected number of animals in each age category. The expected number in the first age category, X, is found by solving the following equation X+(0.51+0.52+0.53+0.54+0.55)X = n where n is the total number of observed animals. The expected values in the remaining categories are determined from the value of X and the hypothesized survival rate.]
Trawling Bycatch
An Alaskan Pollock (Theragra chalcogramma) trawling boat will discontinue trawling in an area if the by-catch of King Salmon (Oncorhynchus tshawytscha) caught in that area exceeds 10% of the catch. In a very large trawl catch the independent observer on the boat randomly sampled 1256 fish and found that 145 were King Salmon. Is there evidence, at the 10% level, that the boat should discontinue trawling in that area?