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Date May Example question Marks available 12 Reference code EXM.2.SL.TZ0.6
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Use and Investigate Question number 6 Adapted from N/A

Question

Jim writes a computer program to generate 500 values of a variable Z. He obtains the following table from his results.

In this situation, state briefly what is meant by

Use a chi-squared goodness of fit test to investigate whether or not, at the 5 % level of significance, the N(0, 1) distribution can be used to model these results.

[12]
a.

a Type I error.

[2]
b.i.

a Type II error.

[2]
b.ii.

Markscheme

          (A1)(A1)(A1)(A1)(A1)(A1)

χ 2 = ( 16 11.35 ) 2 11.35 +           (M1)

= 7.94          A1

Degrees of freedom = 5          A1

Critical value = 11.07          A1

Or use of p-value

We conclude that the data fit the N(0, 1) distribution.          R1

at the 5% level of significance          A1

[12 marks]

a.

Type I error concluding that the data do not fit N(0, 1) when in fact they do.         R2

[2 marks]

b.i.

Type II error concluding that data fit N(0, 1) when in fact they do not.       R2

[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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