7) Compute chi square statistic from following data:
graduate. post graduate
male. 28. 22
female 32 18
Answers
Step-by-step explanation:
Note! The are several ways to phrase these hypotheses. Instead of using the words "independent" and "dependent" one could say "there is no relationship between the two categorical variables" versus "there is a relationship between the two categorical variables." Or "there is no association between the two categorical variables" versus "there is an association between the two variables." The important part is that the null hypothesis refers to the two categorical variables not being related while the alternative is trying to show that they are related.
Once we have gathered our data, we summarize the data in the two-way contingency table. This table represents the observed counts and is called the Observed Counts Table or simply the Observed Table. The contingency table on the introduction page to this lesson represented the observed counts of the party affiliation and opinion for those surveyed.
The question becomes, "How would this table look if the two variables were not related?" That is, under the null hypothesis that the two variables are independent, what would we expect our data to look like?
Consider the following table:
Success Failure Total
Group 1 A B A+B
Group 2 C D C+D
Total A+C B+D A+B+C+D
The total count is . Let's focus on one cell, say Group 1 and Success with observed count A. If we go back to our probability lesson, let denote the event 'Group 1' and denote the event 'Success.' Then,