In a chi-square goodness of fit test for absences across days of the week, if the observed number of absences on Monday is $O$ and the expected number is $E$, what is the contribution of the Monday absences to the calculation of the chi-square test statistic?

• A. $\frac{{E-O}^2}{O}$
• B. $\frac{{O+E}^2}{E}$
• C. $\frac{O^2}{E}$
• D. $\frac{{O-E}^2}{E}$

Answer: (D)

Verified step by step guidance

1. Recall that in a chi-square goodness of fit test, the test statistic is calculated by summing the contributions from each category (in this case, each day of the week).
2. Each category's contribution to the chi-square statistic is given by the formula: \(\frac{(O - E)^2}{E}\), where \(O\) is the observed frequency and \(E\) is the expected frequency for that category.
3. For the Monday absences, identify the observed number of absences as \(O\) and the expected number as \(E\).
4. Substitute these values into the formula to find the contribution of Monday's absences: \(\frac{(O - E)^2}{E}\).
5. This value represents how much the Monday absences contribute to the overall chi-square test statistic, measuring the squared difference between observed and expected counts relative to the expected count.