17.3.7.2 Algorithms (One Sample Proportion Test)One-Prop-algorithm
Hypotheses
Let be the sample size and be the number of events or successes. Then the sample proportion can be expressed:
Let be the sample proportion and the is the hypothetical proportion, this function tests the hypotheses:
vs , for a two-tailed test.
vs , for a lower-tailed test.
vs , for an upper-tailed test.
Normal approximation
P Value
When and , we can compute a p-value using a normal approximation of a binomial distribution. To perform the test, compute the and value by:
,for two tailed test
,for upper tailed test
for lower tailed test
Confidence Interval
confidence level is equal to , the confidence interval for the sample proportion can be generated by:
Null Hypothesis
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Confidence Interval
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Binomial Test
Exact P_value
In Origin, the exact test for one proportion is based on the Binomial Test .
:
Let ,
when
when , where y is the count for z such that and
when , where y is the count for z such that and
Exact Confidence Interval
Exact Confidence interval:
confidence levels is
where denotes the quantile function of Beta distribution.
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