Apps. and Interpretation for IBDP Maths Ebook 1 | Page 344

Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 96
1. Three different fair coins are tossed for 80 times. The following table shows the expected
frequencies and the observed frequencies of the outcomes:
Number of heads 0 1 2 3
Expected frequency 10 30 30 p
Observed frequency 15 27 23 15
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 p .
(c) Write down the degree of freedom of the test.
(d) Find the value of �
2
calc
The critical value is given by 7.815.
, the test statistic.
[1]
[1]
[1]
[2]
(e)
State the conclusion of the test with a reason.
[2]
2. In a contact list of 100 phone numbers, the last digits are recorded. It is expected that the
outcomes are evenly distributed.
The following table shows the frequencies of the outcomes:
Last digit 0 1 2 3 4 5 6 7 8 9
Frequency 10 5 17 5 6 9 13 8 15 12
A
2
� goodness of fit test is conducted at a 5% significance level.
(a)
(b)
(c)
(d)
Write down the null hypothesis of the test.
Write down the value of the expected frequency of each outcome.
Write down the degree of freedom of the test.
Find the value of
�
2
calc
, the test statistic.
[1]
[1]
[1]
[2]
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