LESSON 9: Chi-Square Test

Exercise Problems

1. List the characteristics of a multinomial experiment. How do these characteristics binomial experiment?
2. Calculate the Chi-Square statistic.
3. Could we conclude that the number of calls to the fire department are uniformly distributed over the 24-hour day?

4. Calculate the Chi-Square statistic.

5. Can we conclude that the preference for vanilla ice cream is the same for children as for the population as a whole?

6. Answer problem 13.10b, d on page 792 of the textbook.

13.10 Location of major sports venues, there has been a recent trend for professional sports franchises in Major League Baseball (MLB), the National Football League (NFL), the National Basketball Association (NBA), and the National Hockey League (NHL) to build new stadiums and ballparks in urban, downtown venues. An article in Professional Geographer (Feb. 2000) investigated whether there has been a significant suburban-to-urban shift in the location of major sport facilities. In 1985, 40% of all major sport facilities were located downtown, 30% in central city, and 30% in suburban areas. In contrast, of the 113 major sports franchises that existed in 1997, 58 were built downtown, 26 in central city, and 29 in a suburban area.

(b) Give the null hypothesis for a test to determine whether the proportions of major sports facilities in downtown, central city, and suburban areas in 1997 are the same as in 1985.

(d) Find the value of the chi-square statistic for testing the null hypothesis, part b.

7. Answer problem 13.16 on pages 793-794 of the textbook.

13.16 Butterfly hotspots. Nature (STPT. 1993) reported on a study of animal and plant species "hotspots" in Great Britain. A hotspot is defined as a 10-km ² area that is species-rich, that is, is heavily populated by the species of interest. Analogously, a coldspot is a 10-km ² area that is species-poor. The table gives the number of butterfly hotspots and the number of butterfly coldspots in a sample of 2,588 10-km2 areas. In theory, 5% of the areas should be butterfly hotspots and 5% should be butterfly coldspots, while the remaining areas (90%) are neutral. Test the theory using a = .01.

8. Answer problems 13.22a, b on page 805 of the textbook.

13.22 Consider the accompanying 2x3 contingency table.

1. Specify the null and alternative hypotheses that should be used in testing the independence of the row and column classifications.
2. Specify the test statistic and the rejection region at should be used in conducting the hypothesis test of part a. Use a = .01.
   9. Answer problems 13.22c, d on page 805 of the textbook.
   13.22 Consider the accompanying 2x3 contingency table.
3. Assuming the row classification and the column classification are independent, find estimates for the expected cell counts.
4. Conduct the hypothesis test of part a. Interpret our result.

10. Answer problem 13.34 on pages 808-809 of the textbook.

13.34 Battle simulation trials. In order to evaluate their situational awareness, fighter aircraft pilots participate in battle simulations. At a random point in the trial, the simulator is frozen and data on situation awareness are immediately collected. The simulation is then continued until, ultimately, performance (e.g., number of kills) is measured. A study reported in Human Factors (Mar. 1995) investigated whether temporarily stopping the simulation results in any change in pilot performance. Trials were designed so that some simulations were stopped to collect situation awareness data while others were not stopped. Each trial was then classified according to the number of kills made by the pilot. The data for 180 trials are summarized in the contingency table below. Conduct a contingency table analysis and fully interpret the results.

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