Apps. and Interpretation for IBDP Maths Ebook 1 | Page 351

Exercise 98
1. An environmental scientist catches certain fishes from two different ponds, one from Peru
and another one from Indonesia. The lengths of fishes are recorded and studied, such that
the mean lengths �
1
and �
2
of fishes from Peru and Indonesia respectively are compared.
The following table shows the data:
Length of fishes
from Peru (cm)
Length of fishes
from Indonesia (cm)
22.3 19.8 14.2 23.3 23.9 25.7 20.9
15.2 16.3 21.1 18.4 19.1
A t -test is conducted at a 5% significance level.
(a)
State an assumption of conducting the t -test.
(b) (i) Write down the null hypothesis of the test.
[1]
(c)
(d)
(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]
2. Leo purchased two samples of bottles of milks from two suppliers, Dari and Luna. He
wants to know whether the mean volume �
D
of bottles of milk from Dari is greater than
the mean volume �
L
of bottles of milk from Luna. He measures the volumes precisely
and summarize the data in the following table:
Volume of bottles of
milk from Dari (mL)
Volume of bottles of
milk from Luna (mL)
330 329 330 332 327 329
321 329 328 330 320 323
23
A t -test is conducted at a 5% significance level.
(a)
State an assumption of conducting the t -test.
(b) (i) Write down the null hypothesis of the test.
[1]
(ii)
Write down the alternative hypothesis of the test.
[2]
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