S4 June 2008 Q3
3. The weights, in grams, of mice are normally distributed. A biologist takes a random sample of 10 mice. She weighs each mouse and records its weight.
The ten mice are then fed on a special diet. They are weighed again after two weeks.
Their weights in grams are as follows:
| Mouse | A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|---|
| Weight before diet | 50.0 | 48.3 | 47.5 | 54.0 | 38.9 | 42.7 | 50.1 | 46.8 | 40.3 | 41.2 |
| Weight after diet | 52.1 | 47.6 | 50.1 | 52.3 | 42.2 | 44.3 | 51.8 | 48.0 | 41.9 | 43.6 |
Stating your hypotheses clearly, and using a 1% level of significance, test whether or not the diet causes an increase in the mean weight of the mice. (8)
| Scheme | Marks |
|---|---|
| Differences \(2.1\ \ -0.7\ \ 2.6\ \ -1.7\ \ 3.3\ \ 1.6\ \ 1.7\ \ 1.2\ \ 1.6\ \ 2.4\) | M1 |
| \(\bar{d} = 1.41\) | M1 |
| \(\mathrm{H}_0 : \mu_d = 0 \quad \mathrm{H}_1 : \mu_d \gt 0\) | B1 |
| \(s = \sqrt{\dfrac{40.65 - 10 \times 1.41^2}{9}} = 1.5191\ldots\) | M1 |
| \(t = \dfrac{1.41}{\left(\dfrac{1.519\ldots}{\sqrt{10}}\right)} = 2.935\ldots\) awrt 2.94 / 2.93 | M1 A1 |
| \(t_9(1\%) = 2.821\) | B1 |
| \(2.935.. \gt 2.821\) Evidence to reject \(\mathrm{H}_0\). There has been an increase in the mean weight of the mice. | B1ft |
| (8) |
Notes
2 sample test can score
M0 M0
B1 for \(\mathrm{H}_0 : \mu_A = \mu_B \quad \mathrm{H}_1 : \mu_A \lt \mu_B\)
M1 \(\dfrac{9 \times 24.5 + 9 \times 17.16}{18}\)
M0 A0
B1 2.552
B1 ft
ie 4/8