21M.1.SL.TZ2.8

pestleMathematicsAISLPaper 121M· sl-4-11-expected-observed-hypotheses-chi-squared-gof-t-testsource ↗

At Springfield University, the weights, in $kg$ , of $10$ chinchilla rabbits and $10$ sable rabbits were recorded. The aim was to find out whether chinchilla rabbits are generally heavier than sable rabbits. The results obtained are summarized in the following table.

A $t$ -test is to be performed at the $5 %$ significance level.

Write down the null and alternative hypotheses.

[2]

Find the $p$ -value for this test.

[2]

Write down the conclusion to the test. Give a reason for your answer.

[2]

Markscheme / solution

(let $μ_{c} =$ population mean for chinchilla rabbits, $μ_{s} =$ population mean for sable rabbits)

$H_{0} : μ_{c} = μ_{s}$ A1

$H_{1} : μ_{c} > μ_{s}$ A1

Note: Accept an equivalent statement in words, must include mean and reference to “population mean” / “mean for all chinchilla rabbits” for the first A1 to be awarded.
Do not accept an imprecise “the means are equal”.

[2 marks]

$p$ -value $= 0.0408 (0.0408065 \dots)$ A2

Note: Award A1 for an answer of $0.041565 \dots$ , from “unpooled” settings on GDC.

[2 marks]

$0.0408 < 0.05$ . R1

(there is sufficient evidence to) reject (or not accept) $H_{0}$ A1

(there is sufficient evidence to suggest that chinchilla rabbits are heavier than sable rabbits)

Note: Do not award R0A1. Accept ‘accept $H_{1}$ ’.

[2 marks]

Examiners’ report

[N/A]