S3 June 2006 Q3
3. A biologist investigated whether or not the diet of chickens influenced the amount of cholesterol in their eggs. The cholesterol content of 70 eggs selected at random from chickens fed diet \(A\) had a mean value of 198 mg and a standard deviation of 47 mg. A random sample of 90 eggs from chickens fed diet \(B\) had a mean cholesterol content of 201 mg and a standard deviation of 23 mg.
(a) Stating your hypotheses clearly and using a 5% level of significance, test whether or not there is a difference between the mean cholesterol content of eggs laid by chickens fed on these two diets. (7)
(b) State, in the context of this question, an assumption you have made in carrying out the test in part (a). (2)
| Scheme | Marks |
|---|---|
| \(\mathrm{H}_0 : \mu_A = \mu_B\), \(\mathrm{H}_1 : \mu_A \neq \mu_B\) \(\mu_1, \mu_2\) OK both | B1 |
| \(\text{se} = \sqrt{\dfrac{47^2}{70} + \dfrac{23^2}{90}} \ \left(= \sqrt{37.43492\ldots}\right)\) | M1 A1 |
| Test statistic is \(\pm \dfrac{198 - 201}{\text{se}} = \pm 0.4903\) awrt \(\pm 0.49\) M1 A1 Prob awrt 0.312 B1 Prob cv 0.025 | M1 A1 |
| \(\text{cv} = (\pm)1.96\) | B1 |
| Insufficient evidence to reject \(\mathrm{H}_0\), no significant difference between the mean cholesterol content of the two samples. (require correct comparison for ft) context required. | A1ft |
| (7) |
| Scheme | Marks |
|---|---|
| – require 1 egg from each of 70 chickens of diet \(A\) to ensure independence, similarly for diet \(B\). – no chickens in common between the two samples to ensure independence – not same chickens on diet \(A\) and diet \(B\) because if it were we need to do a paired analysis. Any 1 | B1, B1 |
| (2) | |
| (9 marks) |