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Lecture Statistical techniques in business and economics (14/e): Chapter 17 - Lind, Marchal, Wathen

Chapter 17 - Nonparametric methods: Chi-square applications. In this chapter, the learning objectives are: List the characteristics of the chi-square distribution, conduct a test of hypothesis comparing an observed set of frequencies to an expected distribution, conduct a test of hypothesis to determine whether two classification criteria are related. | Nonparametric Methods: Chi-Square Applications Chapter 17 GOALS List the characteristics of the chi-square distribution. Conduct a test of hypothesis comparing an observed set of frequencies to an expected distribution. Conduct a test of hypothesis to determine whether two classification criteria are related. Characteristics of the Chi-Square Distribution The major characteristics of the chi-square distribution It is positively skewed. It is non-negative. It is based on degrees of freedom. When the degrees of freedom change a new distribution is created. Goodness-of-Fit Test: Equal Expected Frequencies Let f0 and fe be the observed and expected frequencies respectively. H0: There is no difference between the observed and the expected frequencies H1: There is a difference between the observed and the expected frequencies. The test statistic is: The critical value is a chi-square value with (k-1) degrees of freedom, where k is the number of categories EXAMPLE Ms. Jan . | Nonparametric Methods: Chi-Square Applications Chapter 17 GOALS List the characteristics of the chi-square distribution. Conduct a test of hypothesis comparing an observed set of frequencies to an expected distribution. Conduct a test of hypothesis to determine whether two classification criteria are related. Characteristics of the Chi-Square Distribution The major characteristics of the chi-square distribution It is positively skewed. It is non-negative. It is based on degrees of freedom. When the degrees of freedom change a new distribution is created. Goodness-of-Fit Test: Equal Expected Frequencies Let f0 and fe be the observed and expected frequencies respectively. H0: There is no difference between the observed and the expected frequencies H1: There is a difference between the observed and the expected frequencies. The test statistic is: The critical value is a chi-square value with (k-1) degrees of freedom, where k is the number of categories EXAMPLE Ms. Jan Kilpatrick is the marketing manager for a manufacturer of sports cards. She plans to begin selling a series of cards with pictures and playing statistics of former Major League Baseball players. One of the problems is the selection of the former players. At a baseball card show at Southwyck Mall last weekend, she set up a booth and offered cards of the following six Hall of Fame baseball players: Tom Seaver, Nolan Ryan, Ty Cobb, George Brett, Hank Aaron, and Johnny Bench. At the end of the day she sold a total of 120 cards. The number of cards sold for each old-time player is shown in the table on the right. Can she conclude the sales are not the same for each player? Use 0.05 significance level. Step 1: State the null hypothesis and the alternate hypothesis. H0: there is no difference between fo and fe H1: there is a difference between fo and fe Step 2: Select the level of significance. α = 0.05 as stated in the problem Step 3: Select the test statistic. The test statistic follows the .