The confidence interval is a way to report the most probable value for a population’s mean μ, when the population’s standard deviation, δ is known. Confidence intervals can be quoted for any desired probability level, several samples of which are shown in the table below.

z | Confidence interval (%) |
---|---|

0.50 | 38.30 |

1.00 | 68.26 |

1.50 | 86.64 |

1.96 | 95.00 |

2.00 | 95.44 |

2.50 | 98.76 |

3.00 | 99.73 |

3.50 | 99.95 |

There are 3 methods for calculating confidence interval and their application is dependent on the type of data provided.

**Method 1: Confidence interval (CI) given population mean and variance**

What is the 95% confidence interval for the amount of aspirin in a single analgesic tablet drawn from a population where μ is 250mg and δ² is 25?

*solution*

Xi = μ ± zδ

μ=250mg

z=1.96(the value corresponding to 95% on the table above)

δ=5

Xi= μ ± 1.96δ

250mg ± (1.96)(5)

=250mg ± 10mg