A social scientist investigated whether there is an association between regular exercise (Yes/No) and high self-rated well-being (Yes/No). They conducted a Chi-square test of association on the collected data. Part of the calculation table is shown below.
| Cell | Observed frequency (O) | Expected frequency (E) | O – E | (O – E)2^22 | (O – E)2^22 / E |
|---|---|---|---|---|---|
| A | 20 | 15.00 | 5.00 | 25.00 | 1.67 |
| B | 20 | 25.00 | –5.00 | 25.00 | 1.00 |
| C | 10 | 15.00 | –5.00 | 25.00 | 1.67 |
| D | 30 |
Formula for χ2\chi^2χ2:
χ2=∑(O−E)2E \chi^2 = \sum \frac{(O - E)^2}{E} χ2=∑E(O−E)2Calculate the overall value of Chi-square (χ2\chi^2χ2). Show your workings.
