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%.

${H_0}:\mu  = 5.5;{\text{ }}{H_1}:\mu  \ne 5.5$     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]