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Lecture notes Commercial maths (Scma) Statistics for Management and Economics
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INTRODUCTIONTO HYPOTHESIS
TESTING
CHAPTER 2
By Setsweke Nkwane, Commercial Mathematics, Hypothesis Testing
, Concepts of Hypothesis Testing
■ A hypothesis test is a process that uses sample statistics to test
claim about the value of a population parameter.
■ A statistical hypothesis is verbal statement, or claim, about
population parameter is called a There are two general procedures f
making inferences about population:
A hypothesis test involves two hypotheses: the Null Hypothesis an
Alternative
■ A null hypothesis is a statistical hypothesis to be tested. We use th
symbol H0 to represent the null hypothesis.
■ An alternative hypothesis s the complement of the null hypothesis.
is a statement that must be true if H0 is false. We use the symbol Ha
H1 to represent the alternative hypothesis.
■ At the end of the test, one of two decisions will be made: 1. reject th
null hypothesis, or 2. fail to reject the null hypothesis.
By Setsweke Nkwane, Commercial Mathematics, Hypothesis Testing
, Stating a Hypothesis
The hypothesis tests about a population parameter may take o
three forms: the first uses an equality in the null hypothesis
last two use inequalities in the null hypothesis;. For hypoth
tests involving a population mean, we let 𝜇0 denote
hypothesized value and we must choose one of the following t
forms for the hypothesis test.
𝐻0 : 𝜇 = 𝜇0 𝐻0 : 𝜇 ≤ (=)𝜇0 𝐻0 : 𝜇 ≥ (=)
𝐻𝑎 : 𝜇 ≠ 𝜇0 𝐻𝑎 : 𝜇 > 𝜇0 𝐻𝑎 : 𝜇 < 𝜇0
By Setsweke Nkwane, Commercial Mathematics, Hypothesis Testing
, Three choices are possible for the alternative hypothesis.
■ If the primary concern is deciding whether a population, 𝜇, is different from
specified value 𝜇0 , we express the alternative hypothesis as
𝐻𝑎 : 𝜇 ≠ 𝜇0
A hypothesis test whose alternative hypothesis has this form is called a two-tailed/side
test.
■ If the primary concern is deciding whether a population, 𝜇, is greater than a specifie
value 𝜇0 , we express the alternative hypothesis as
𝐻𝑎 : 𝜇 > 𝜇0
A hypothesis test whose alternative hypothesis has this form is called a right-tailed/side
test.
■ If the primary concern is deciding whether a population, 𝜇, is less than a specifie
value 𝜇0 , we express the alternative hypothesis as
𝐻𝑎 : 𝜇 < 𝜇0
A hypothesis test whose alternative hypothesis has this form is called a left-tailed/side
test.
By Setsweke Nkwane, Commercial Mathematics, Hypothesis Testing
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