Apps. and Interpretation for IBDP Maths Ebook 1 | Page 343

96
Paper 1 – Goodness of Fit Test
Example
In an experiment, a fair six-sided die is tossed for 240 times. It is expected that the
outcomes are evenly distributed.
The following table shows the frequencies of the outcomes:
Outcome 1 2 3 4 5 6
Frequency 36 58 48 44 30 24
A
2
� goodness of fit test is conducted at a 5% significance level.
(a) Write down the null hypothesis of the test.
(b) Write down the value of the expected frequency of each outcome.
(c) Write down the degree of freedom of the test.
(d) Find the value of �
2
calc
The critical value is given by 11.070.
, the test statistic.
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[2]
(e)
State the conclusion of the test with a reason.
[2]
Solution
23
(a) H
0
: The outcomes are evenly distributed. A1 N1
(b) 40 A1 N1
(c) 5 A1 N1
(d) 19.4 A2 N2
(e) The null hypothesis is rejected. A1
2
As � � 11.070 . A1 N2
calc
[1]
[1]
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[2]
[2]
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