Page 50 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 5 Hypothesis Testing
A sample mean that falls close to the hypothesised value of 3 kg would be considered evidence in favour of
H . Conversely, a sample mean that is significantly less than or more than 3 kg would be evidence favouring
–
0
H . A critical region, indicated by the shaded areas in the figure 5.2, is arbitrarily chosen to be X , 2.7 and
–
–
1
X . 3.3. If the sample mean X falls inside the critical region, H is rejected; otherwise H is not rejected.
0 0
 –

–
2 2
–
x
2.7  = 3.0 3.3
Critical region Nonrejection region Critical region
Figure 5.2

The significance level of the test is equal to the total of the areas shaded in each tail of the normal distribution.
We have, – –
a = P(X , 2.7) + P(X . 3.3).
–
–
The z values corresponding to x = 2.7 and x = 3.3 are
1 2
z = 2.7 – 3.0 = –1.5
1 0.2
z = 3.3 – 3.0 = 1.5
2 0.2
Hence,
a = P(Z , –1.5) + P(Z . 1.5)
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= 2P(Z , –1.5)
= 0.1336

That is to say 13.36% of all samples of size 64 would lead to the rejection of H when it is true.
0
One-tailed test (H : µ < 3 or µ > 3)
1
The critical region for the alternative hypothesis H : µ , 3 lies entirely in the left tail of the normal
1
distribution, while the alternative hypothesis µ . 3 lies entirely in the right tail as shown in Figure 5.3.

5

 
– –
x
x
Critical region  = 3.0  = 3.0 Critical region
Figure 5.3 (a) Figure 5.3(b)
In testing hypothesis about a continuous population, it is common to choose the value of a to be 1%, 5%
and 10%.

What is
Hypothesis
Testing?
INFO

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05 STPM Math(T) T3.indd 241 28/10/2021 10:24 AM