1. Define the following terms: A. Contingency table B. Chi-square test 2. List the assumptions required to perform...

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1. Define the following terms:
A. Contingency table
B. Chi-square test
2. List the assumptions required to perform a chi-squaretest?

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solution 1 Contingency Table A twoway table also called a contingency table is a useful tool for examining relationships between categorical variables The entries in the cells of a twoway table can be frequency counts or relative frequencies just like a oneway table Dance Sports TV Total Men 2 10 8 20 Women 16 6 8 30 Total 18 16 16 50 The twoway table above shows the favorite leisure activities for 50 adults 20 men and 30 women Because entries in the table are frequency counts the table is a frequency table B 1 ChiSquare Goodness of Fit Test A chisquare goodness of fit test attempts to answer the following question Are sample data consistent with a hypothesized distribution The test is appropriate when the following conditions are met The sampling method is simple random sampling The population is at least 10 times as large as the sample The variable under study is categorical The expected value for each level of the variable is at least 5 Here is how to conduct the test Define hypotheses For a chisquare goodness of fit test the hypotheses take the following form H0 The data are consistent with a specified distribution Ha The data are not consistent with a specified distribution Typically the null hypothesis specifies the proportion of observations at each level of the categorical variable The alternative hypothesis is that at least one of the specified proportions is not true Specify significance level Often researchers choose significance levels equal to 001 005 or 010 but any value between 0 and 1 can be used Find degrees of freedom The degrees of freedom DF is equal to the number of levels k of the categorical variable minus one DF k 1 Compute expected frequency counts The expected frequency counts at each level of the categorical variable are equal to the sample size times the See Answer

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