Page 65 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 5 Hypothesis Testing

Summary

1. A hypothesis test or significance test is a method of using sample data as evidence to test a statistical
hypothesis about a population parameter.

2. A null hypothesis is a statement about a population parameter that is assumed to be true until it is
rejected with strong evidence obtained from a sample. An alternative hypothesis is a statement about
a population parameter that will be true if the null hypothesis is rejected.
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3. A test statistic is a random variable whose value is used to determine whether a null hypothesis is
rejected in a hypothesis test.
4. A critical region is the set of values that leads to the rejection of the null hypothesis in favour of the
alternative hypothesis.

5. (a) Type I error occurs if the null hypothesis is rejected when the null hypothesis is true. The
probability of making this error is called the significance level of a test denoted by a.
(b) Type II error occurs if the null hypothesis is not rejected while in fact the null hypothesis is
false. The probability of making this error is denoted by b.

6. A hypothesis test which has one sided critical region in either left or right tail is called a one-tailed
test. A hypothesis test which has two critical regions, each at the left tail and right tail, is called a
two-tailed test.

7. The general test procedure is as follows:
• State the null and alternative hypotheses
• Specify the significance level
• Select an appropriate probability distribution and determine the critical region(s)
• Calculate the value of the test statistic
• Make a decision
–
8. To test a hypothesis about a population mean with known variance the test statistic is Z = X – µ ,
σ
where the population is normal if the sample size is small. 
n
9. To test a hypothesis about a population mean with unknown variance where the sample is large, the
–
5 test statistic is Z = X – µ .
^
σ

n
10. To test a hypothesis about a population proportion, where the sample size is small, the critical region(s)
is (are) as follows:
(a) All x values such that P(X < x) , a for p , p 0
(b) All x values such that P(X > x) , a for p . p 0
(c) All x values such that P(X < x) , a when x , np and all x values such that P(X > x) < a
2
2
0
when x . np for p ≠ p
0 0
11. To test hypothesis about a population proportion, where the sample size is large, the test statistic is
p – p
^
Z = .
p(1 – p)
n
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05 STPM Math(T) T3.indd 256 28/10/2021 10:24 AM