Final answer:
The most appropriate statistic for measuring the relationship between someone passing or failing a class and membership or non-membership in an honor society is the chi-square test for independence. The test determines whether there is a significant association between two categorical variables. It involves gathering data, creating a contingency table, calculating expected frequencies, and interpreting the results of the test.
Step-by-step explanation:
The most appropriate statistic for measuring the relationship between someone passing or failing a class and membership or non-membership in an honor society is the chi-square test for independence.
The chi-square test for independence is used to determine whether there is a significant association between two categorical variables. In this case, the variables are passing/failing a class and membership/non-membership in an honor society.
To conduct the chi-square test for independence, you would gather data on the number of students who passed or failed the class and the number of students who are members or non-members of the honor society. You would then create a contingency table and calculate the expected frequencies based on the null hypothesis of independence. Finally, you would perform the chi-square test and interpret the results to determine if there is a significant relationship between passing/failing a class and membership/non-membership in an honor society.