The One-sample Binomial Test test is used to test if the sample was drawn from a population with a proportion equal to some hypothesized value. Both exact and approximate tests may be performed.
Hypotheses
The following hypotheses may be tested:
![Prop-1sample Hyp](/help/GZ/MONTH/help/images/Prop-1sampleHyp.jpg)
Where
is the true population proportion from which the sample was drawn, and
is the hypothesized population value.
Assumptions
- The sample has been randomly drawn from the population (Critical)
- The population may be modeled with a binomial distribution, which has these attributes:
- Only two possible outcomes or classifications occur with each item examined (Critical)
- The probability of occurrence of each classification remains fixed from item to item over time (Critical)
- The probability of occurrence of each item sampled is independent of all other items sampled (Critical)
Test Statistics
Approximate Test
![Prop1sampleAprox](/help/GZ/MONTH/help/images/Prop1sampleAprox.jpg)
Where the +/- sign is determined as follows for the above hypothesis:
![Prop1sampleAproxSign](/help/GZ/MONTH/help/images/Prop1sampleAproxSign.jpg)
Exact Test
![Prop1sampleExact](/help/GZ/MONTH/help/images/Prop1sampleExact.jpg)
Output
![Prop-1sampleOutput](/help/GZ/MONTH/help/images/Prop-1sampleOutput.jpg)
Note
The p-value is flagged with an asterisk (*) when p <= alpha.