| Date | May 2017 | Marks available | 4 | Reference code | 17M.1.hl.TZ0.1 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Calculate | Question number | 1 | Adapted from | N/A |
Question
The mean weight of a certain breed of bird is claimed to be 5.5 kg. In order to test this claim, a random sample of 10 birds of the breed was obtained and weighed, with the following results in kg.
\[5.41\quad \quad \quad 5.22\quad \quad \quad 5.54\quad \quad \quad 5.58\quad \quad \quad 5.20\quad \quad \quad 5.57\quad \quad \quad 5.23\quad \quad \quad 5.32\quad \quad \quad 5.46\quad \quad \quad 5.37\]
You may assume that the weights of this breed of bird are normally distributed.
State suitable hypotheses for testing the above claim using a two-tailed test.
Calculate unbiased estimates of the mean and the variance of the weights of this breed of bird.
Determine the \(p\)-value of the above data.
State whether or not the claim is supported by the data, using a significance level of 5%.
Markscheme
\({H_0}:\mu = 5.5;{\text{ }}{H_1}:\mu \ne 5.5\) A1
[1 mark]
\(\sum {x = 53.9,{\text{ }}\hat \mu = 5.39} \) (M1)A1
\(\sum {{x^2} = 290.7132,{\text{ }}{{\hat \sigma }^2} = 0.0214} \) (M1)A1
Note: Accept any answer that rounds correctly to 0.021.
[4 marks]
attempt to use the \(t\)-test (M1)
\(t = - 2.38{\text{ }}({\text{Accept }} + 2.38)\) (A1)
\({\text{DF}} = 9\) (A1)
\(p{\text{ - value}} = 0.0412\) A1
[??? marks]
the claim is not supported (not accepted, rejected) at the 5% level of significance A1
[??? marks]
