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    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. | Weight of chinchilla rabbits, kg | 4.9 | 4.2 | 4.1 | 4.4 | 4.3 | 4.6 | 4.0 | 4.7 | 4.5 | 4.4 |

    Question
    SLPaper 1

    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. | Weight of chinchilla rabbits, kg | 4.9 | 4.2 | 4.1 | 4.4 | 4.3 | 4.6 | 4.0 | 4.7 | 4.5 | 4.4 | | Weight of sable rabbits, kg | 4.2 | 4.1 | 4.1 | 4.2 | 4.5 | 4.4 | 4.5 | 3.9 | 4.2 | 4.0 | A ttt-test is to be performed at the 5% significance level.

    1.

    Write down the null and alternative hypotheses.

    [2]
    Verified
    Solution

    (let μc=\mu_{\mathrm{c}}=μc​= population mean for chinchilla rabbits, μs=\mu_{\mathrm{s}}=μs​= population mean for sable rabbits) H0:μc=μsH_{0}: \mu_{\mathrm{c}}=\mu_{\mathrm{s}}H0​:μc​=μs​ (A1) H1:μc>μsH_{1}: \mu_{\mathrm{c}}>\mu_{\mathrm{s}}H1​:μc​>μs​ (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\boldsymbol{A1}A1 to be awarded. Do not accept an imprecise "the means are equal".

    2.

    Find the ppp-value for this test.

    [2]
    Verified
    Solution

    ppp-value =0.0408(0.0408065…)=0.0408(0.0408065 \ldots)=0.0408(0.0408065…) (A1) Note: Award A1\boldsymbol{A1}A1 for an answer of 0.041565…0.041565 \ldots0.041565…, from "unpooled" settings on GDC.

    3.

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

    [2]
    Verified
    Solution

    0.0408<0.050.0408<0.050.0408<0.05 (R1) (there is sufficient evidence to) reject (or not accept) H0H_{0}H0​ (A1) (there is sufficient evidence to suggest that chinchilla rabbits are heavier than sable rabbits) Note: Do not award R0A1. Accept 'accept H1H_{1}H1​'.

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