BUSINESS STATISTICS 6 -1 Hypothesis Testing
6 Hypothesis Testing
• Using Statistics
• Statistical Hypothesis Testing
• A Two-Tailed, Large-Sample Test for the Population Mean
• A Two-Tailed, Small-Sample Test for the Population Mean
• A Two-Tailed, Large-Sample Test for the Population Proportion
• One-Tailed Tests
• The p-Value
• The probability of a Type II Error and the Power of the Test
• Using the Computer
• Summary and Review of Terms
ernational University – School of Business Assoc. Prof. Ho Thanh Phong
, BUSINESS STATISTICS 6 -2 Hypothesis Testing
6.1. Introduction
• A hypothesis is a statement or assertion about the state of nature
(about the true value of an unknown population parameter):
– The accused is innocent
– =100
• Every hypothesis implies its contradiction or alternative:
– The accused is guilty
– 100
• A hypothesis is either true or false, and you may fail to reject it
or you may reject it on the basis of information:
– Trial testimony and evidence
– Sample data
ernational University – School of Business Assoc. Prof. Ho Thanh Phong
, BUSINESS STATISTICS 6 -3 Hypothesis Testing
6.2. Decision-Making
• One hypothesis is maintained to be true until a decision is
made to reject it as false:
– Guilt is proven “beyond a reasonable doubt”
– The alternative is highly improbable
• A decision to fail to reject or reject a hypothesis may be:
– Correct
• A true hypothesis may not be rejected
» An innocent defendant may be acquitted
• A false hypothesis may be rejected
» A guilty defendant may be convicted
– Incorrect
• A true hypothesis may be rejected
» An innocent defendant may be convicted
• A false hypothesis may not be rejected
» A guilty defendant may be acquitted
ernational University – School of Business Assoc. Prof. Ho Thanh Phong
, BUSINESS STATISTICS 6 -4 Hypothesis Testing
6.3. Type of Hypothesis
• A null hypothesis, denoted by H0, is an assertion about one or more
population parameters. This is the assertion we hold to be true until
we have sufficient statistical evidence to conclude otherwise.
H0: =100 ; H0: 100
• The alternative hypothesis, denoted by H1, is the assertion of all
situations not covered by the null hypothesis.
H1: 100; H1: 100
• H0 and H1 are:
– Mutually exclusive
Only one can be true.
– Exhaustive
Together they cover all possibilities, so one or the other must be true.
ernational University – School of Business Assoc. Prof. Ho Thanh Phong
6 Hypothesis Testing
• Using Statistics
• Statistical Hypothesis Testing
• A Two-Tailed, Large-Sample Test for the Population Mean
• A Two-Tailed, Small-Sample Test for the Population Mean
• A Two-Tailed, Large-Sample Test for the Population Proportion
• One-Tailed Tests
• The p-Value
• The probability of a Type II Error and the Power of the Test
• Using the Computer
• Summary and Review of Terms
ernational University – School of Business Assoc. Prof. Ho Thanh Phong
, BUSINESS STATISTICS 6 -2 Hypothesis Testing
6.1. Introduction
• A hypothesis is a statement or assertion about the state of nature
(about the true value of an unknown population parameter):
– The accused is innocent
– =100
• Every hypothesis implies its contradiction or alternative:
– The accused is guilty
– 100
• A hypothesis is either true or false, and you may fail to reject it
or you may reject it on the basis of information:
– Trial testimony and evidence
– Sample data
ernational University – School of Business Assoc. Prof. Ho Thanh Phong
, BUSINESS STATISTICS 6 -3 Hypothesis Testing
6.2. Decision-Making
• One hypothesis is maintained to be true until a decision is
made to reject it as false:
– Guilt is proven “beyond a reasonable doubt”
– The alternative is highly improbable
• A decision to fail to reject or reject a hypothesis may be:
– Correct
• A true hypothesis may not be rejected
» An innocent defendant may be acquitted
• A false hypothesis may be rejected
» A guilty defendant may be convicted
– Incorrect
• A true hypothesis may be rejected
» An innocent defendant may be convicted
• A false hypothesis may not be rejected
» A guilty defendant may be acquitted
ernational University – School of Business Assoc. Prof. Ho Thanh Phong
, BUSINESS STATISTICS 6 -4 Hypothesis Testing
6.3. Type of Hypothesis
• A null hypothesis, denoted by H0, is an assertion about one or more
population parameters. This is the assertion we hold to be true until
we have sufficient statistical evidence to conclude otherwise.
H0: =100 ; H0: 100
• The alternative hypothesis, denoted by H1, is the assertion of all
situations not covered by the null hypothesis.
H1: 100; H1: 100
• H0 and H1 are:
– Mutually exclusive
Only one can be true.
– Exhaustive
Together they cover all possibilities, so one or the other must be true.
ernational University – School of Business Assoc. Prof. Ho Thanh Phong
