Binomial test for a single proportion - overview
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Binomial test for a single proportion
|One categorical with 2 independent groups|
|H0: $\pi = \pi_0$
Here $\pi$ is the population proportion of 'successes', and $\pi_0$ is the population proportion of successes according to the null hypothesis.
|H1 two sided: $\pi \neq \pi_0$|
H1 right sided: $\pi > \pi_0$
H1 left sided: $\pi < \pi_0$
|$X$ = number of successes in the sample|
|Sampling distribution of $X$ if H0 were true|
|Binomial($n$, $P$) distribution.
Here $n = N$ (total sample size), and $P = \pi_0$ (population proportion according to the null hypothesis).
|Is the proportion of smokers amongst office workers different from $\pi_0 = 0.2$?|
|Analyze > Nonparametric Tests > Legacy Dialogs > Binomial...
|Frequencies > 2 Outcomes - Binomial test