Six Sigma Glossary from MiC Quality
Hypothesis Tests for Proportions
 Comparing Proportions

This test is used for large samples to test the hypothesis:

H0: the proportion is the same in both populations
H1: the proportions are different/the proportion is greater for process 1 than process 2

The value of the Z statistic is calculated from:

where:

p1 and p2: the proportions in each sample
X1 and X2: the number possessing the characteristic in each sample
n1 and n2: the sample size

The p-value can be obtained from Excel using the function:

one-tail test: = 1 - NORMSDIST(Z0)
two-tail test: = (1 - NORMSDIST(Z0))/2

Alternatively the critical values can be found in the t-tables.

 Hypothesis Test for Proportions

For large samples, refer to the tests "Comparing Proportions" and "Proportions Against a Specified Value". For small sample sizes refer to Chi-Square tests.

 Proportion Against a Specified Value

This test is used for large samples to test the hypothesis:

H0: the proportion is the same in both populations
H1: the proportion is [different to/greater than/less than] the specified value

The value of the Z statistic is calculated from:

Where:

the proportion in the sample
the specified value of the proportion

n the sample size

The p-value can be obtained from Excel using the function:

one-tail test: = 1 - NORMSDIST(Z0)
two-tail test: = (1 - NORMSDIST(Z0))/2

Alternatively the critical values can be found in the t-tables.

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