Page 63 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 5 Hypothesis Testing

This is a one-tailed test with a critical region located at the left tail. The area
of the critical region is 0.05. To locate the z value, we look for 0.05 area in the
normal distribution table. From the table, the z value is –1.645.
The critical regions: z , –1.645.

Step 4 : Calculate the value of the test statistic.
^ p – p
z =
p(1 – p)
Penerbitan Pelangi Sdn Bhd. All Rights Reserved.
n

= 0.07 – 0.15
0.15(1 – 0.15)
100
= –2.240

Step 5 : Make a decision.
We compare the value of the test statistic to the critical value. This value of
z = –2.240 is smaller than the critical value of –1.645 and thus it falls in the
critical region. We reject H and this evidence is sufficient to conclude that the
0
process has been improved at the 5% significance level.

Exercise 5.3

1. In a random sample of 20 independent observations obtained from a binomial distribution, a student
wants to test H : p = 0.3 versus H : p ≠ 0.3. The student decides to reject H if X < 3 or X > 11.
1
0
0
0
Find P(X < 3) and P(X > 11).
2. Suppose that X = 13 is a number of occurrence from a sample of 20 independent observations obtained
from a binomial population. Test the following hypotheses at the 10% significance level.
H : p = 0.8
0
H : p , 0.8
5 1
3. A hunter claims that he hits 70% of the wildfowl he shoots at. On one day he guns down 6 of the 12
wildfowls he aims at. Using the 5% significance level for a hypothesis test, what is your conclusion on
this claim?

4. If there is no gender bias in trainee selection, then the pool of potential trainees is 50% male and
50% female. In a sample of 10 trainees, it is found that there are only two women trainees. Is there
evidence of gender bias in trainee selection? Use the 10% significance level for the hypothesis test.

5. A magazine claims that 45% of its readers do not trust an advertisement on a certain health food
product. In a poll of 20 randomly sampled magazine readers conducted two years later, 11 state that
they do not trust the advertisement. At the 5% significance level, is there evidence to support the claim
that the percentage of the readers against the advertisement has increased?

254

05 STPM Math(T) T3.indd 254 28/10/2021 10:24 AM