Determine unbiased estimates for $\mu$ and ${\sigma ^2}$.

Use a two-tailed test to determine the $p$-value for the above results.

Interpret your $p$-value at the 5% level of significance, justifying your conclusion.

UE of $\mu$ is $8.01{\text{ }}( = 8.0125)$     A1

UE of ${\sigma ^2}$ is 0.404     (M1)A1

Note:     Accept answers that round correctly to 2 sf.

Note:      Condone incorrect notation, ie, $\mu$ instead of UE of $\mu$ and ${\sigma ^2}$ instead of UE of ${\sigma ^2}$.

Note:     M0 for squaring $0.594 \ldots$ giving 0.354, M1A0 for failing to square $0.635 \ldots$

[3 marks]

attempting to use the $t$-test     (M1)

$p$-value is 0.0566     A2

Note:     Accept any answer that rounds correctly to 2 sf.

[3 marks]

$0.0566 > 0.05$     R1

we accept the null hypothesis (mean pumpkin weight is 7.5 kg)     A1

Note:     Apply follow through on the candidate’s $p$-value.

Note:     Do not award A1 if R1 is not awarded.

[2 marks]