Apps. and Interpretation for IBDP Maths Ebook 1 | Page 363

2. A social work is investigating whether organizing an anti-smoking event in public can
decrease the mean smoking rates of citizens. The table below shows some samples of the
number of times for a person to smoke in a day before the anti-smoking event and after
the anti-smoking event:
Before anti-smoking event 12 8 15 7 3 10 16
After anti-smoking event 1 4 6 4 1
Let �
1
and �
2
be the mean number of times for a person to smoke in a day before the
anti-smoking event and after the anti-smoking event respectively. A t -test is conducted at
a 1% significance level, and it is assumed that the variances of the scores for two
examinations are the same.
(a) State an assumption of conducting the t -test.
(b) Write down the alternative hypothesis of the test.
(c) Find the p -value.
(d) Write down the value of t , the t -statistic.
(e) State the conclusion of the test with a reason.
A record is randomly selected from the above 12 records.
[1]
[1]
[2]
[1]
[2]
(f) (i) Find the probability that the score is from the after anti-smoking
event and is an even number.
(ii)
Given that the selected record is at least 4, find the probability that the
score is from the after anti-smoking event.
Three records are randomly selected from the above 12 records.
[4]
23
(g)
Find the probability that all of them are even numbers.
[3]
353
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