## Question 4(i):

| Answer | Marks | Guidance |
|--------|-------|----------|
| $H_0$: no association between age and working days lost $H_1$: some association between age and working days lost | B1 | For hypotheses, at least one of which is in context. Allow hypotheses in terms of independence, in context. Do not allow "relationship" or "correlation" for "association". |
| Expected values table: Under 35: 24.47, 28.39, 9.14; 35 to 50: 26.84, 31.14, 10.02; Over 50: 23.68, 27.47, 8.84 | B1 | For at least one row/column of expected values correct (to 1 d.p.). Seen or implied by contributions. |
| All expected values correct (to 2 d.p.) | B1 | All correct (to 2 d.p.). Accept fraction equivalents. Seen or implied by contributions. |
| Contributions table: Under 35: 1.7404, 0.0680, 2.8880; 35 to 50: 0.0499, 0.0239, 0.4076; Over 50: 2.4931, 0.0101, 5.7945 | M1 | For valid attempt at $(O-E)^2/E$. Seen or implied by at least one correct contribution to 2 d.p. Allow 5.80 for last cell. Condone values in a list. |
| $X^2 = 13.48$ | A1 | For all correct to 2 d.p. or better. Allow 5.80 for last cell. Condone values in a list. NB: These two marks cannot be implied by a correct final value of $X^2$. |
| $X^2 = 13.48$ | B1 | For answers rounding to 13.48. Do not penalize over-specification. |
| Refer to $\chi^2_4$ | B1 | For 4 degrees of freedom. |
| Critical value at 1% level $= 13.28$ | B1 | No further marks from here if incorrect. |
| $13.48 > 13.28$ so result is significant | B1* | For significant oe. FT their test statistic. |
| There is evidence to **suggest** that there is some association between age and working days lost | E1dep* | For **non-assertive** conclusion in context. Allow conclusion in terms of independence. FT their test statistic. NB if $H_0\ H_1$ reversed, or 'correlation' mentioned, do not award final E1. |
| **[10]** | | |

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## Question 4(ii):

| Answer | Marks | Guidance |
|--------|-------|----------|
| The large contribution of 2.4931 implies that there are fewer employees than expected who lose 0 to 4 working days. | E1 | For correct interpretation with reference to contribution for 0 to 4 working days. |
| The small contribution of 0.0101 implies that there are about as many as expected who lose 5 to 9 working days. | E1 | For correct interpretation with reference to contribution for 5 to 9 working days. |
| The large contribution of 5.7945 implies that there are more employees than expected who lose more than 10 working days. | E1 | For correct interpretation with reference to contribution for more than 10 working days. SC1 if all interpretations are correct but with no reference to contributions, i.e. max 1 out of 3. |
| **[3]** | | |

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## Question 4(iii):

| Answer | Marks | Guidance |
|--------|-------|----------|
| Critical value at 1% level $= 9.21$ | B1* | CAO for cv. |
| $7.08 < 9.21$ so the result is not significant oe | B1dep* | For correct conclusion. |
| There is insufficient evidence to **suggest** that there is an association between age and working days lost. | E1dep* | For **non-assertive** conclusion in context. |
| **[3]** | | |

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## Question 4(iv):

| Answer | Marks | Guidance |
|--------|-------|----------|
| Conclusion in (iii) is valid if only categorizing working days lost into '0 to 4' and '5 or more'. | E1 | As written, or for explaining that **combining/subdividing groups** leads to a **different** result. |
| However, if '5 or more' is subdivided into '5 to 9' and '10 or more', this additional subdivision gives the data more precision and allows the relationship in part (i) to be revealed. | E1 | For **subdivision** allows relationship to be revealed or gives more precision/sensitivity/detail. Allow subdivision gives "a more reliable test" but not "a more accurate test". For both to be awarded, wording must be **clear**. |
| **[2]** | | |