Apps. and Interpretation for IBDP Maths Ebook 1 | Page 362

Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 100
1. A teacher wants to know whether the supplementary lessons between the mock
examination and the official examination can improve students’ mean score in the official
examination. The table below shows the scores (out of 100) of some students in two
examinations:
Mock exam score 47 53 85 76 80 65 68 90 77
Official exam score 35 50 58 92 97 93 88 61 89 79
Let �
1
and �
2
be the mean scores of the mock examination and the official examination
respectively. A t -test is conducted at a 10% significance level, and it is assumed that the
variances of the scores for two examinations are the same.
(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 score is randomly selected from the above 19 scores.
(e)
Given that the selected score is at least 80, find the probability that the score is
from the mock examination.
One score from each examination is randomly selected.
[2]
[2]
[1]
[2]
[2]
(f) (i) Find the probability that both of them are greater than 75.
(ii) Find the probability that at most one of them are greater than 75.
[4]
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