Next section: Mean, σ known

An excellent way to specify the precision is to construct a confidence interval. If the number of digits remembered for the 10 students were: 4, 4, 5, 5, 5, 6, 6, 7, 8, 9 then the estimated value of μ would be 5.9 and the 95% confidence interval would range from 4.71 to 7.09. (Click here to see how to compute the interval.)

The wider the interval, the more confident you are that it contains the parameter. The 99% confidence interval is therefore wider than the 95% confidence interval and extends from 4.19 to 7.61.

Below are shown some examples of possible confidence intervals. Although the parameter μ

Lower Limit | Parameter | Upper Limit | ||
---|---|---|---|---|

0.2 |
≤ |
π |
≤ |
0.7 |

-3.2 |
≤ |
μ |
≤ |
4.5 |

3.5 |
≤ |
μ _{1} - μ_{2} |
≤ |
7.9 |

0.4 |
≤ |
π |
≤ |
0.8 |

0.3 |
≤ |
π _{1} - π_{2} |
≤ |
0.7 |

Next section: Mean, σ known