A researcher conducted a study on the relationship between study environment (quiet vs noisy) and exam performance (pass vs fail). Below is the partial table of observed and expected frequencies used to calculate a Chi-square statistic.
Calculate the expected frequency for cell D. Present your answer to two decimal places and show your workings.
| Cell | Observed frequency (OOO) | Expected frequency (EEE) | O−EO - EO−E | (O−E)2(O - E)^2(O−E)2 | (O−E)2/E(O - E)^2 / E(O−E)2/E |
|---|---|---|---|---|---|
| A (Quiet/Pass) | 15 | 11.78 | 3.22 | 10.37 | 0.88 |
| B (Quiet/Fail) | 8 | 11.22 | -3.22 | 10.37 | 0.92 |
| C (Noisy/Pass) | 6 | 9.22 | -3.22 | 10.37 | 1.12 |
| D (Noisy/Fail) | 12 |
Formula for χ2\chi^2χ2:
χ2=∑(O−E)2E \chi^2 = \sum \frac{(O - E)^2}{E} χ2=∑E(O−E)2513 exam-style questions on OCR A Level Psychology Data recording, analysis and presentation. Each one has a worked solution and a mark scheme showing where the marks go.