Question 6.EX.2: The following data show the observed and expected frequencie...
The following data show the observed and expected frequencies of an experiment with four possible outcomes, A–D.
| Outcome | A | B | C | D |
| Observed | 40 | 60 | 75 | 90 |
| Expected | 35 | 55 | 75 | 100 |
Test the hypothesis that the results are in line with expectations using the 5% significance level.
The calculation of the test statistic is
| Outcome | Observed | Expected | O − E | (O − E)² | \frac {(O−E)^{2}}{E} |
| A | 40 | 35 | 5 | 25 | 0.714 |
| B | 60 | 55 | 5 | 25 | 0.455 |
| C | 75 | 75 | 0 | 0 | 0 |
| D | 90 | 100 | −10 | 100 | 1 |
| Total | 2.169 |
This is smaller than the critical value of 7.81 so the null is not rejected.
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