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[ Pobierz caÅ‚ość w formacie PDF ] Section 11-4 introduced McNemar s test for testing the null hypothesis that a sample of matched pairs of data comes from a population in which the discordant (different) pairs occur in the same proportion. The following are some key components of the methods discussed in this chapter: Ï% Section 11-2 (Test for goodness-of-fit): sO 2 Ed2 Test statistic is x2 5 g E Test is right-tailed with k 2 1 degrees of freedom. All expected frequencies must be at least 5. Ï% Section 11-3 (Contingency table test of independence or homogeneity): sO 2 Ed2 Test statistic is x2 5 g E Test is right-tailed with (r 2 1)(c 2 1) degrees of freedom. All expected frequen- cies must be at least 5. Ï% Section 11-4 (2 3 2 table with frequencies from matched pairs of data): su b 2 c u21d2 Test statistic is x2 5 b 1 c where the frequencies of b and c must come from discordant pairs. Test is right- tailed with 1 degree of freedom. The frequencies b and c must be such that b 1 c $ 10. Statistical Literacy and Critical Thinking 1. Categorical Data This chapter introduced a few different methods for the analysis of categorical data. What are categorical data? 2. Conducting a Survey A student conducts a research project by asking 200 classmates if they have had a credit card stolen. She constructs a contingency table with row cat- egories of gender (male>female) and column categories of response (yes, no, refused to answer). She uses the methods of Section 11-3 to conclude that gender is indepen- dent of response. What is wrong with her project? 3. Chi-Square Distribution This chapter presented different methods involving applica- tion of the chi-square distribution. Which of the following properties of a chi-square distribution are true? a. Values of a chi-square test statistic are always positive or zero, but never negative. b. A chi-square distribution is symmetric. c. There is a different chi-square distribution for each number of degrees of freedom. 5014_TriolaE/S_CH11pp588-633 1/19/07 9:57 AM Page 629 Review Exercises 629 d. When using a chi-square distribution, the number of degrees of freedom is always the sample size minus 1. e. When using the chi-square distribution, sample data need not be random if the sample size is very large. 4. Checking Requirements The methods of testing for goodness-of-fit and the methods of testing for independence between two variables used for a contingency table re- quire that all expected frequencies must be at least 5. Can those methods be used if there is a cell with an observed frequency count less than 5? Why or why not? Review Exercises 1. Are DWI Fatalities the Result of Weekend Drinking? Many people believe that fatal DWI crashes occur because of casual drinkers who tend to binge on Friday and Satur- day nights, whereas others believe that fatal DWI crashes are caused by people who drink every day of the week. In a study of fatal car crashes, 216 cases are randomly selected from the pool in which the driver was found to have a blood alcohol content over 0.10. These cases are broken down according to the day of the week, with the re- sults listed in the accompanying table (based on data from the Dutchess County STOP-DWI Program). At the 0.05 significance level, test the claim that such fatal crashes occur on the different days of the week with equal frequency. Does the evi- dence support the theory that fatal DWI car crashes are due to casual drinkers or that they are caused by those who drink daily? Day Sun Mon Tues Wed Thurs Fri Sat Number 40 24 25 28 29 32 38 2. E-Mail and Privacy Workers and senior-level bosses were asked if it was seriously unethical to monitor employee e-mail, and the results are summarized in the table (based on data from a Gallup poll). Use a 0.05 significance level to test the claim that the response is independent of whether the subject is a worker or a senior-level boss. Does the conclusion change if a significance level of 0.01 is used instead of 0.05? Do workers and bosses appear to agree on this issue? Yes No Workers 192 244 Bosses 40 81 3. Crime and Strangers The accompanying table lists survey results obtained from a random sample of different crime victims (based on data from the U.S. Department of Justice). At the 0.05 significance level, test the claim that the type of crime is inde- pendent of whether the criminal is a stranger. How might the results affect the strat- egy police officers use when they investigate crimes? Homicide Robbery Assault Criminal was a stranger 12 379 727 Criminal was an acquaintance or relative 39 106 642 4. Comparing Treatments Two different creams are used to treat subjects with poison ivy irritation on both hands. Each subject is given a treatment of Ivy Ease on one hand while their other hand is treated with a placebo. The sample results are summarized in the table below. Use a 0.05 significance level to test the null hypothesis that the fol- lowing two proportions are the same: (1) the proportion of subjects with relief on the hand treated with Ivy Ease and no relief on the hand treated with a placebo; (2) the 5014_TriolaE/S_CH11pp588-633 11/18/05 8:23 AM Page 630 630 Chapter 11 Multinomial Experiments and Contingency Tables proportion of subjects with no relief on the hand treated with Ivy Ease and relief on the hand treated with a placebo. Does the Ivy Ease treatment appear to be effective? Treatment with Ivy Ease Relief No Relief Relief 12 8 Placebo No relief 32 19 Cumulative Review Exercises [ Pobierz caÅ‚ość w formacie PDF ] |