Apps. and Interpretation for IBDP Maths Ebook 1 | Page 360

Your Practice Set – Applications and Interpretation for IBDP Mathematics
100
Paper 2 – Problems Involving -Test
Example
In a library, the habit of reading books of young people is investigated. The table below
shows the number of fiction books read by two different groups of people in a particular
month, after they have filled in a survey:
The group of
13-year-old students
The group of
23-year-old people
5 6 5 4 7 9 5 3 2 4
1 3 2 7 2 4 2 1
The library manager wants to investigate whether 13-year-old students read more than
23-year-old people on average. Let �
1
and �
2
be the mean number of fiction books read
by the 13-year-old students and the 23-year-old people respectively. A t -test is
conducted at a 5% significance level.
(a) (i) Write down the null hypothesis of the test.
(b)
(c)
(d)
(ii)
Write down the alternative hypothesis of the test.
Find the p -value.
Write down the value of t , the t -statistic.
State the conclusion of the test with a reason.
A person is randomly selected from the above 18 people.
(e)
Given that the selected person reads at least four fiction books, find the
probability that the person is 13 years old.
One person from each age group above is randomly selected.
[2]
[2]
[1]
[2]
[2]
(f) (i) Find the probability that both of them read less than four fiction books.
(ii)
Find the probability that at least one of them read less than four fiction
books.
[4]
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