21M.1.SL.TZ1.6

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

Arriane has geese on her farm. She claims the mean weight of eggs from her black geese is less than the mean weight of eggs from her white geese.

She recorded the weights of eggs, in grams, from a random selection of geese. The data is shown in the table.

In order to test her claim, Arriane performs a $t$ -test at a $10 %$ level of significance. It is assumed that the weights of eggs are normally distributed and the samples have equal variances.

State, in words, the null hypothesis.

[1]

Calculate the $p$ -value for this test.

[2]

State whether the result of the test supports Arriane’s claim. Justify your reasoning.

[2]

Markscheme / solution

EITHER

$H_{0} :$ The population mean weight of eggs from (her/the) black geese is equal to/the same as the population mean weight of eggs from (her/the) white geese.

$H_{0} :$ The population mean weight of eggs from (her/the) black geese is not less than the population mean weight of eggs from (her/the) white geese. A1

Note: Reference to the "population mean weight" must be explicit for the A1 to be awarded. The term “population” can be implied by use of “all” or “on average” or “generally” when relating to the weight of eggs e.g. “the mean weight of eggs for all (her/the) black geese”.
Award A0 if reference is made to the mean weights from the sample or the table.
Award A0 for a null hypothesis written in symbolic form.

[1 mark]

$p$ -value $= 0.177 (0.176953 \dots)$ A2

Note: Award A1 for an answer of $0.18221 \dots$ , from “unpooled” settings on GDC.

[2 marks]

$0.177 > 0.1$ R1

(insufficient evidence to reject $H_{0}$ )

Arriane’s claim is not supported by the evidence A1

Note: Accept $p > 0.1$ or $p >$ significance level provided $p$ is explicitly seen in part (b). Award A1 only if reference is specifically made to Arriane's claim.
Do not award R0A1.

[2 marks]

Examiners’ report

[N/A]