- Complete a chi-square test for goodness of fit and write its conclusion in context of the problem
Chi-Square ([latex]\chi^2[/latex]) Test Statistic
As with other hypothesis tests, we need to be able to model the variability we expect in samples if the null hypothesis is true. Then, we can determine whether the chi-square test statistic from the data is unusual or typical.
An unusual [latex]\chi^2[/latex] value suggests that there are statistically significant differences between the sample data and the null distribution and provides evidence against the null hypothesis. This is the same logic we have been applying with hypothesis testing.
The following is the formula for the chi-square test statistic:
[latex]\chi^2=\sum\dfrac{(\text{Observed}-\text{Expected})^2}{\text{Expected}}[/latex]
Sample C was the actual sample obtained by researchers in the study mentioned previously, and it satisfies the conditions for a chi-square goodness of fit test.
| Sample C |
Quarter 1 (Jan. – March) |
Quarter 2 (April – June) |
Quarter 3 (July – Sept.) |
Quarter 4 (Oct. – Dec.) |
| Observed number of football players | 507 | 534 | 389 | 273 |
Does this sample provide enough evidence to reject the null hypothesis and support the alternative hypothesis? Let’s investigate.
Step 2: Choose the appropriate degrees of freedom (number of categories – 1) and select the “Upper Tail” probability type.
Step 3: Enter the calculated chi-square statistic ([latex]\chi^2=147[/latex]).
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