Apps. and Interpretation for IBDP Maths Ebook 1 | Página 354

Your Practice Set – Applications and Interpretation for IBDP Mathematics
99
Paper 2 – Problems Involving Chi-Squared Test
Example
The curriculum coordinator of a high school is going to investigate whether there is a
relationship between the gender of a student and the choice of school overseas trip
selected by the student. There are in total four choices of the overseas trip: Canada, USA,
Mexico and Costa Rica.
80 students are asked to complete a survey about their preferences, and the following
table shows the distribution of the results:
Gender
Choices of overseas trips
Canada USA Mexico Costa Rica
Male 10 22 4 4
Female 7 12 8 13
A
2
� test for independence is conducted at a 5% significance level.
(a) (i) Write down the null hypothesis of the test.
(ii) Write down the alternative hypothesis of the test.
(b) Write down the degree of freedom of the test.
(c) Find the value of �
2
calc
, the test statistic.
The critical value is given by 7.815.
(d) State the conclusion of the test with a reason.
One student is selected at random.
[2]
[1]
[2]
[2]
(e) (i) Find the probability that the student is a male student and he chooses
Costa Rica.
(ii)
(iii)
Find the probability that the student chooses Canada.
Given that the student chooses USA, find the probability that the student is
a female.
[6]
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