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Date November Example question Marks available 3 Reference code EXN.2.AHL.TZ0.3
Level Additional Higher Level Paper Paper 2 Time zone Time zone 0
Command term Find Question number 3 Adapted from N/A

Question

Dana has collected some data regarding the heights h (metres) of waves against a pier at 50 randomly chosen times in a single day. This data is shown in the table below.

She wishes to perform a χ2-test at the 5% significance level to see if the height of waves could be modelled by a normal distribution. Her null hypothesis is

H0: The data can be modelled by a normal distribution.

From the table she calculates the mean of the heights in her sample to be 0.828m and the standard deviation of the heights sn to be 0.257m.

She calculates the expected values for each interval under this null hypothesis, and some of these values are shown in the table below.

Use the given value of sn to find the value of sn-1.

[2]
a.

Find the value of a and the value of b, giving your answers correct to one decimal place.

[3]
b.

Find the value of the χ2 test statistic χcalc2 for this test.

[2]
c.

Determine the degrees of freedom for Dana’s test.

[2]
d.

It is given that the critical value for this test is 9.49.

State the conclusion of the test in context. Use your answer to part (c) to justify your conclusion.

[2]
e.

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.

sn-1=5049×0.257        (M1)

 

Note: M1 is for the use of the correct formula

 

=0.260        A1

 

[2 marks]

a.

Using x¯=0.828 and sn-1=0.260        (M1)

a=7.3, b=7.6        A1A1

 

[3 marks]

b.

χcalc2=3.35        (M1)A1

 

[2 marks]

c.

Combining columns with expected values less than 5 leaves 7 cells       (M1)

7-1-2=4        A1

 

[2 marks]

d.

3.35<9.49       R1

hence insufficient evidence to reject H0 that the heights of the waves are normally distributed.       A1

 

Note: The A1 can be awarded independently of the R1.

 

[2 marks]

e.

Examiners report

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

Syllabus sections

Topic 4—Statistics and probability » SL 4.9—Normal distribution and calculations
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Topic 4—Statistics and probability

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