S3 January 2006 Q4
4. People over the age of 65 are offered an annual flu injection. A health official took a random sample from a list of patients who were over 65. She recorded their gender and whether or not the offer of an annual flu injection was accepted or rejected. The results are summarised below.
| Gender | Accepted | Rejected |
|---|---|---|
| Male | 170 | 110 |
| Female | 280 | 140 |
Using a 5% significance level, test whether or not there is an association between gender and acceptance or rejection of an annual flu injection. State your hypotheses clearly. (9)
| Scheme | Marks | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\mathrm{H}_0\) : No association between gender and acceptance \(\mathrm{H}_1\) : gender and acceptance are associated | B1 | ||||||||||||||||
| M1 A1 | ||||||||||||||||
| |||||||||||||||||
| \(\displaystyle\sum \frac{(O - E)^2}{E} = 2.59\) (Yates’ 2.34) (Condone use of Yates’) | M1 A1 | ||||||||||||||||
| \(\nu = 1\); (5%) = 3.841 | B1; B1 | ||||||||||||||||
| \(3.841 \gt 2.59\). There is insufficient evidence to reject \(\mathrm{H}_0\) There is no association between a persons gender and their acceptance (of the offer of a flu jab.) | M1 A1ft | ||||||||||||||||
| (9) | |||||||||||||||||
| (9 marks) |