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Date November Example question Marks available 2 Reference code EXN.1.SL.TZ0.3
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term State Question number 3 Adapted from N/A

Question

The weights of apples on a tree can be modelled by a normal distribution with a mean of 85 grams and a standard deviation of 7.5 grams.

A sample of apples are taken from 2 trees, A and B, in different parts of the orchard.

The data is shown in the table below.

The owner of the orchard wants to know whether the mean weight of the apples from tree A(μA) is greater than the mean weight of the apples from tree B(μB) so sets up the following test:

H0:μA=μB and H1:μA>μB

Find the probability that an apple from the tree has a weight greater than 90 grams.

[2]
a.

Find the p-value for the owner’s test.

[2]
b.i.

The test is performed at the 5% significance level.

State the conclusion of the test, giving a reason for your answer.

[2]
b.ii.

Markscheme

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

Let the weight of an apple be X

PX>90=0.252  0.252492        (M1)A1

 

[2 marks]

a.

p-value =0.0189  (0.018947)       (M1)A1

 

[2 marks]

b.i.

0.0189<0.05        R1

Sufficient evidence to reject the null hypothesis (that the weights of apples from the two trees are equal)        A1

 

[2 marks]

b.ii.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.

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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