Apps. and Interpretation for IBDP Maths Ebook 1 | Page 364

Your Practice Set – Applications and Interpretation for IBDP Mathematics
3. Samantha is a History teacher teaching the class A and the class B. She is comparing the
performances of students in both classes in the History monthly assessments. The tables
below show the scores (out of 100) of some students in both classes in the assessments in
January and February:
Class A
Assessment in January 58 92 67 72 73 80 85 77 69
Assessment in February 90 32 97 45 62 60 50 74
Class B
Assessment in January 65 68 58 57 70 49 79
Assessment in February * * * * * * * * *
Let �
A1
and �
B1
be the mean scores of the class A and class B respectively, in the
assessment in January. The first t -test is conducted at a 5% significance level to test
whether the mean scores of two classes are different.
(a)
(b)
(c)
State an assumption of conducting the t -test.
Write down the alternative hypothesis of this test.
Find the p -value.
[2]
(d) Write down the value of t , the t -statistic.
[1]
(e) State the conclusion of the test with a reason.
[2]
Let �
A2
be the mean score of the class A in the assessment in February. The second t -
test is conducted at a 5% significance level to test whether the mean score of the class A
increases, and it is assumed that the variances of the scores for both assessments in class
A are the same.
[1]
[1]
(f) (i) Write down the alternative hypothesis of this test.
(ii)
Using the p -value approach to state the conclusion.
[4]
For the above scores of the assessment in January, one score from each class is randomly
selected.
(g)
Find the probability that only one of them is between 55 and 75 inclusive.
[3]
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