Construct a 95% confidence interval for the proportion value p from a population of 40 and a sample size of 12

p^ - zscore

X = sample mean, s = sample standard deviation, zscore = Normal distribution Z-score from a probability where α = (1 - Confidence Percentage)/2

p^ = | n |

N |

p^ = | 12 |

40 |

p^ = 0.3

σ_{p} = | √p^(1 - p^) |

√N |

σ_{p} = | √0.3(1 - 0.3) |

√40 |

σ_{p} = | √0.3(0.7) |

√40 |

σ_{p} = | √0.21 |

√40 |

σ

σ

α = 1 - Confidence%

α = 1 - 0.95

α = 0.05

α = ½(α)

α = ½(0.05)

α = 0.025

Find z-score for α value for 0.025

zscore

MOE = σ

MOE = 0.947 x 1.96

MOE = 0.

High End = p^+ zscore

High End = 0.3 + 1.96 * 0.947

High End = 0.3 + 0.

High End = 0.442

Low End = p^ - zscore

Low End = 0.3 - 1.96 * 0.947

Low End = 0.3 - 0.

Low End = 0.158

What this means is if we repeated experiments, the proportion of such intervals that contain p would be 95%