EXM.1.SL.TZ0.7

pestleMathematicsAISLPaper 1EXM· sl-4-11-expected-observed-hypotheses-chi-squared-gof-t-testsource ↗

Anita is concerned that the construction of a new factory will have an adverse affect on the fish in a nearby lake. Before construction begins she catches fish at random, records their weight and returns them to the lake. After the construction is finished she collects a second, random sample of weights of fish from the lake. Her data is shown in the table.

Anita decides to use a t-test, at the 5% significance level, to determine if the mean weight of the fish changed after construction of the factory.

State an assumption that Anita is making, in order to use a t-test.

[1]

State the hypotheses for this t-test.

[1]

Find the p-value for this t-test.

[3]

State the conclusion of this test, in context, giving a reason.

[2]

Markscheme / solution

EITHER

The weights of the fish are distributed normally. A1

The variance of the two groups of fish is equal. A1

[1 mark]

${H_0}\,{\text{:}}\,\bar B = \bar A$ and ${H_1}\,{\text{:}}\,\bar B \ne \bar A$ A1

where B and A represent the weights before and after.

[1 mark]

df = 14, t = 0.861 (M1)

p-value = 0.403 A2

[3 marks]

Since 0.403 > 0.05 R1

Do not reject H₀.

There is insufficient evidence, at the 5% level, of a change in weight. A1

[2 marks]

Examiners’ report

[N/A]