**MOE Formula**

= z * √p * (1 - p) / √n

Where: z is z-score (a critical value) for a confidence level Percentage,

p = proportion,

N = population size,

n = sample size.

**MOE Formula (with finite Population Correction)**

= z * √p * (1 - p) / √(N - 1) * n / (N - n)

Where: z is z-score (a critical value) for a confidence level Percentage,

p = proportion,

N = population size,

n = sample size.

**More information**

**Population Size:** The total number of people whose opinion or behaviour your sample will represent.

**Confidence Level (%):** The Probability that your sample accurately reflects the attitudes of your population.The industry standard is 95%.

**Sample Size:**Number of people who look your survey.

**Margin of Error (%):** The range (measured as a percentage) that your populations response may deviate from your samples.

## z value

Our calculator used the following z-score values.

Confidence Level | z-score |
---|---|

70% | 1.04 |

75% | 1.15 |

80% | 1.28 |

85% | 1.44 |

90% | 1.645 |

91% | 1.7 |

92% | 1.75 |

93% | 1.81 |

94% | 1.88 |

95% | 1.96 |

96% | 2.05 |

97% | 2.17 |

98% | 2.33 |

99% | 2.576 |

99.5% | 2.807 |

99.9% | 3.29 |

99.99% | 3.89 |

## MOE Real Time Example Question and Derivation:

1000 people were surveyed and 380 thought that natural disasters was not caused by human pollution.

Find the Margin of Error for a 90% confidence interval ?

**Step 1:**Find P-hat by dividing the number of people who responded positively. In this case, 380/1000 people (38%) responded positively.

**Step 2:**Find the z-score that goes with the given confidence interval 90% , you get a z-score (a critical value) of 1.645.

**Step 3:**Insert the values into the formula and solve:

MOE = z * √p * (1 - p) / √(N - 1) * n / (N - n)

Where: z = 1.645, Proportion Percentage (P) = 38% Sample size (n) = 1000 evel of 90%

MOE = 1.645 * √0.38 * (1-0.38)/ √1000

MOE = 0.798/31.623 * 100

The margin of error is **±2.525%**