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Date May Example question Marks available 2 Reference code EXM.1.SL.TZ0.7
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term State and Give a reason Question number 7 Adapted from N/A

Question

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]
a.

State the hypotheses for this t-test.

[1]
b.

Find the p-value for this t-test.

[3]
c.

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

[2]
d.

Markscheme

EITHER

The weights of the fish are distributed normally.          A1

OR

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

[1 mark]

a.

H 0 : B ¯ = A ¯ and  H 1 : B ¯ A ¯          A1

where B and A represent the weights before and after.

[1 mark]

b.

df = 14,  t = 0.861         (M1)

p-value = 0.403         A2

[3 marks]

c.

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]

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.

Syllabus sections

Topic 4—Statistics and probability » SL 4.11—Expected, observed, hypotheses, chi squared, gof, t-test
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Topic 4—Statistics and probability

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