S3 June 2016 Q2
2. A new drug to vaccinate against influenza was given to 110 randomly chosen volunteers. The volunteers were given the drug in one of 3 different concentrations, \(A\), \(B\) and \(C\), and then were monitored to see if they caught influenza. The results are shown in the table below.
| \(A\) | \(B\) | \(C\) | |
|---|---|---|---|
| Influenza | 12 | 29 | 9 |
| No influenza | 15 | 23 | 22 |
Test, at the 10% level of significance, whether or not there is an association between catching influenza and the concentration of the new drug. State your hypotheses and show your working clearly. You should state your expected frequencies to 2 decimal places. (10)
| Scheme | Marks | ||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\mathrm{H_0}\): Drug concentration and catching influenza are independent / not associated \(\mathrm{H_1}\): Drug concentration and catching influenza are not independent / associated | B1 | ||||||||||||||||||||||||||||
| M1A1 | ||||||||||||||||||||||||||||
| M1A1 | ||||||||||||||||||||||||||||
| \(\displaystyle\sum \frac{(O - E)^2}{E} = 5.6145\ldots\) or \(\displaystyle\sum \frac{O^2}{E} - N = 115.62\ldots - 110 = 5.6145\ldots\) awrt 5.61-5.62 | A1 | ||||||||||||||||||||||||||||
| \(\nu = (3 - 1)(2 - 1) = 2\), \(\chi^2_2(10\%) = 4.605\) | B1B1ft | ||||||||||||||||||||||||||||
| Reject \(\mathrm{H_0}\) | M1 | ||||||||||||||||||||||||||||
| Drug concentration and catching influenza are not independent / are associated. | A1cao | ||||||||||||||||||||||||||||
| (10 marks) |
Notes
B1 hyps correct way around
M1 for correct expression at least once
A1 all seen and correct 2dp or better. Can be implied by test statistic of awrt 5.61-5.62.
M1 either method at least one correct
A1 at least 3 correct values. Can be implied by test statistic of awrt 5.61-5.62
A1 awrt 5.61-5.62
B1 cao
B1 follow through their \(\nu\)
M1 must correctly reject / not reject the null hypothesis based on their test stat and cv oe