Apps. and Interpretation for IBDP Maths Ebook 1 | Page 350

Your Practice Set – Applications and Interpretation for IBDP Mathematics
98
Paper 1 – -test
Example
Robin purchased two samples of circular iron plates from two factories A and B. He
wants to know whether the mean radius �
A
and �
B
of circular iron plates from Factory
A and Factory B respectively are different. The following table shows the values of radii
from the samples:
Radii of plates
from Factory A (cm)
Radii of plates
from Factory B (cm)
12.1 12.3 12.9 12.7
11.9 11.7 11.1 11.0 11.0 12.0 12.5
A t -test is conducted at a 2% significance level.
(a)
State an assumption of conducting the t -test.
(b) (i) Write down the null hypothesis of the test.
[1]
(c)
(d)
Solution
(ii) Write down the alternative hypothesis of the test.
Find the p -value.
State the conclusion of the test with a reason.
[2]
[2]
[2]
(a) The radii of plates are normally distributed. A1 N1
(b) (i) H
0
: �A � �B
A1 N1
[1]
(ii) H
1
: �A � �B
A1 N1
(c) p-value � 0.0121929154
(A1) for correct value
p-value � 0.0122
A1 N2
(d) The null hypothesis is rejected. A1
As p-value � 0.02 . A1 N2
[2]
[2]
[2]
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