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Date May 2021 Marks available 1 Reference code 21M.1.SL.TZ2.11
Level Standard Level Paper Paper 1 Time zone Time zone 2
Command term Find Question number 11 Adapted from N/A

Question

A newspaper vendor in Singapore is trying to predict how many copies of The Straits Times they will sell. The vendor forms a model to predict the number of copies sold each weekday. According to this model, they expect the same number of copies will be sold each day.

To test the model, they record the number of copies sold each weekday during a particular week. This data is shown in the table.

A goodness of fit test at the 5% significance level is used on this data to determine whether the vendor’s model is suitable.

The critical value for the test is 9.49 and the hypotheses are

H0: The data satisfies the model.
H1: The data does not satisfy the model.

Find an estimate for how many copies the vendor expects to sell each day.

[1]
a.

Write down the degrees of freedom for this test.

[1]
b.i.

Write down the conclusion to the test. Give a reason for your answer.

[4]
b.ii.

Markscheme

74+97+91+86+1125=92             A1


[1 mark]

a.

4             A1


[1 mark]

b.i.

χ2calc=8.54  8.54347  OR  p-value =0.0736  (0.0735802)          A2

8.54<9.49  OR  0.0736>0.05             R1

therefore there is insufficient evidence to reject H0        A1

(i.e. the data satisfies the model)


Note: Do not award R0A1. Accept “accept” or “do not reject” in place of “insufficient evidence to reject”.
          Award the R1 for comparing their p-value with 0.05 or their χ2 value with 9.49 and then FT their final conclusion.


[4 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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