- Calculate and describe the value of a chi-square statistics in context of a real-world problem
- Write a null and alternative hypothesis for a chi-square test
[latex]\chi^2[/latex] Test Statistic
Imagine that Harvard claims: “We only accept the top academic applicants, and we treat those applicants equally. Our admitted class is as good as a random sample from the distribution of top academic applicants.”
You would like to decide if there’s convincing evidence against this claim.
- Formally, the null hypothesis, [latex]H_0[/latex], is that the distribution of the admitted group is the same as the distribution of the top academic applicants.
- The alternative hypothesis, [latex]H_A[/latex], is that the distribution of the admitted group is different than the distribution of the top academic applicants.
The following is the formula for the chi-square test statistic:
[latex]\chi^2=\sum\dfrac{(\text{Observed}-\text{Expected})^2}{\text{Expected}}[/latex]