S3 June 2009 Q2
2. The heights of a random sample of 10 imported orchids are measured. The mean height of the sample is found to be 20.1 cm. The heights of the orchids are normally distributed.
Given that the population standard deviation is 0.5 cm,
A grower claims that the mean height of this type of orchid is 19.5 cm.
| Scheme | Marks |
|---|---|
| Limits are \(20.1 \pm 1.96 \times 0.5\) | M1 B1 |
| (19.1, 21.1) | A1cso |
| (3) |
Notes
M1 for \(20.1 \pm z \times 0.5\). Need 20.1 and 0.5 in correct places with no \(\sqrt{10}\)
B1 for \(z = 1.96\) (or better)
A1 for awrt 19.1 and awrt 21.1 but must have scored both M1 and B1
[Correct answer only scores 3/3]
| Scheme | Marks |
|---|---|
| 98 % confidence limits are \(20.1 \pm 2.3263 \times \dfrac{0.5}{\sqrt{10}}\) | M1 B1 |
| (19.7, 20.5) | A1A1 |
| (4) |
Notes
M1 for \(20.1 \pm z \times \dfrac{0.5}{\sqrt{10}}\), need to see 20.1, 0.5 and \(\sqrt{10}\) in correct places
B1 for \(z = 2.3263\) (or better)
1st A1 for awrt 19.7
2nd A1 for awrt 20.5
[Correct answer only scores M1B0A1A1]
| Scheme | Marks |
|---|---|
| The growers claim is not correct | B1 |
| Since 19.5 does not lie in the interval (19.7, 20.5) | dB1 |
| (2) | |
| (9 marks) |
Notes
1st B1 for rejection of the claim. Accept “unlikely” or “not correct”
2nd dB1 Dependent on scoring 1st B1 in this part for rejecting grower’s claim for an argument that supports this. Allow comment on their 98% CI from (b)