BUSINESS STATISTICS 7-1 Comparison two populations
7 The Comparison of Two Populations
• Paired-Observation and Independent sampling
• A Test for the Difference between Two Population
Means Using Independent Random Samples
• A Test for the Difference between Two Population
Means, Assuming Equal Population Variances
• A Large-Sample Test for the Difference between
Two Population Proportions
• The F Distribution and a Test for the Equality of
Two Population Variances
• Using the Computer
• Summary and Review of Terms
ernational University – School of Business Assoc. Prof. Ho Thanh Phong
, BUSINESS STATISTICS 7-2 Comparison two populations
7.1. Introduction
• Inferences about differences between parameters of two
populations
- Paired-Observations
Observe the same group of persons or things
– At two different times: “before” and “after”
– Under two different sets of circumstances or “treatments”
– Independent Samples
Observe different groups of persons or things, at different
times or under different sets of circumstances
ernational University – School of Business Assoc. Prof. Ho Thanh Phong
, BUSINESS STATISTICS 7-3 Comparison two populations
Guide for studying
Paired comparison Independent
Sampling
About the Mean: Small Large Small Large
- Hypothesis Testing sample sample sample sample
- Confidence Interval
About the Variance: F test
- Hypothesis Testing
- Confidence Interval CI for ratio only
About the Proportion: Large sample
- Hypothesis Testing only
- Confidence Interval
ernational University – School of Business Assoc. Prof. Ho Thanh Phong
, BUSINESS STATISTICS 7-4 Comparison two populations
7.2. Comparisons of Means Using
Paired-Observation
Small Sample Large Sample
Hypothesis H0: µD = D (or µD < D) H0: µD = D (or µD < D)
H1: µD ≠ D (or µD ≥ D) H1: µD ≠ D (or µD ≥ D)
[Usually D = 0] [Usually D = 0]
Test D D D D
tt zt
statistics sD n sD n
Decision Reject Null Hypothesis if Reject Null Hypothesis if
t t t n 1, / 2 or t t t n 1, / 2 z t z / 2 or z t z / 2
( t t t n 1, ) ( zt z )
D is the sample average differences between each pair of observations,
sD is sample standard deviation of these differences, sample size n.
D is the two-population differences mean.
ernational University – School of Business Assoc. Prof. Ho Thanh Phong
7 The Comparison of Two Populations
• Paired-Observation and Independent sampling
• A Test for the Difference between Two Population
Means Using Independent Random Samples
• A Test for the Difference between Two Population
Means, Assuming Equal Population Variances
• A Large-Sample Test for the Difference between
Two Population Proportions
• The F Distribution and a Test for the Equality of
Two Population Variances
• Using the Computer
• Summary and Review of Terms
ernational University – School of Business Assoc. Prof. Ho Thanh Phong
, BUSINESS STATISTICS 7-2 Comparison two populations
7.1. Introduction
• Inferences about differences between parameters of two
populations
- Paired-Observations
Observe the same group of persons or things
– At two different times: “before” and “after”
– Under two different sets of circumstances or “treatments”
– Independent Samples
Observe different groups of persons or things, at different
times or under different sets of circumstances
ernational University – School of Business Assoc. Prof. Ho Thanh Phong
, BUSINESS STATISTICS 7-3 Comparison two populations
Guide for studying
Paired comparison Independent
Sampling
About the Mean: Small Large Small Large
- Hypothesis Testing sample sample sample sample
- Confidence Interval
About the Variance: F test
- Hypothesis Testing
- Confidence Interval CI for ratio only
About the Proportion: Large sample
- Hypothesis Testing only
- Confidence Interval
ernational University – School of Business Assoc. Prof. Ho Thanh Phong
, BUSINESS STATISTICS 7-4 Comparison two populations
7.2. Comparisons of Means Using
Paired-Observation
Small Sample Large Sample
Hypothesis H0: µD = D (or µD < D) H0: µD = D (or µD < D)
H1: µD ≠ D (or µD ≥ D) H1: µD ≠ D (or µD ≥ D)
[Usually D = 0] [Usually D = 0]
Test D D D D
tt zt
statistics sD n sD n
Decision Reject Null Hypothesis if Reject Null Hypothesis if
t t t n 1, / 2 or t t t n 1, / 2 z t z / 2 or z t z / 2
( t t t n 1, ) ( zt z )
D is the sample average differences between each pair of observations,
sD is sample standard deviation of these differences, sample size n.
D is the two-population differences mean.
ernational University – School of Business Assoc. Prof. Ho Thanh Phong
