validation message

Hypotheses

H_{0}: P ≥ = ≤ P_{0}

H_{1}: P < ≠ > P_{0}

Test statistic

Normal distribution

Binomial distribution - the probability for event is identical | |

P_{0} the expected population probability |

p̂ the sample probabilities or x the number of successes | |

n - Sample size |

The following R code should produce the same results:

The prop.test uses the Chi-squared statistic with one degree of freedom, which is **exactly** as using the Z test: z^{2}=χ^{2}(1)