Page 54 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 5 Hypothesis Testing

–
1
2
P –z a , X – µ 0 , z a = 1 – a
σ
—
—
2
2

n
This expression can be used to indicate a nonrejection region for the null hypothesis H . Hence,
0
if –z a , z , z a , we do not reject H . On the other hand, if the calculated value of the test statistic falls in
—
0
—
2
2
the critical region, that is, z , –z a or z . z a , H is rejected.
2 — — 0
2
For a fixed significance level a, the critical regions and critical values are as shown in Figure 5.4.
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 (z)
1 – 

– 
2 –
2
z
–z  – 0 z – 
2 2
Figure 5.4
The following two examples illustrate how hypothesis tests are performed for the case in which the population
varience is known.
Example 5

A survey made by the Human Resource Ministry states that the average monthly salary of an executive
is RM4100 with a standard deviation of RM680. However, a sample of 25 executives selected recently
gives an average monthly salary per month of RM3850. Assuming that the average monthly salary of an
executive is normaly distributed, test, at the 1% significance level, whether the ministry’s claim is too high.

Solution: Let μ be the mean monthly salary of an executive claimed by the Human
–
Resource Ministry and x be the corresponding sample mean. Given information:
–
μ = RM4100, σ = RM680, n = 25, x = RM3850.
We are going to test whether the ministry’s claim of monthly salary is too high.
The significance level a is 0.01.
We carry out a hypothesis test using the following five steps. 5

Step 1 : State the null hypothesis and the alternative hypothesis.
H : μ = RM4100,
0
H : μ , RM4100.
1
Step 2 : Specify the significance level.
a = 0.01.

Step 3 : Select an appropriate probability distribution and determine the critical
region.
The population standard deviation s is known, the sample size is small but the
–
population distribution is normal. Hence, the sampling distribution of X is normal
σ
with mean µ and standard deviation  n . We will use the normal distribution
to perform the test.

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05 STPM Math(T) T3.indd 245 28/10/2021 10:24 AM