## One-sided CI

If you are interested in the confidence interval bounded only from the above or the below, you need one-sided confidence intervals for the population mean . Suppose the sample mean and the sample standard deviation from data of sample size . With the confidence level , we can obtain the one-sided CI only with upper or lower bound.

One-sided with upper bound | |

One-sided with lower bound |

If the standard deviation is known, we set and replace the critical point with of the standard normal distribution.

There is an interesting relationship between confidence intervals (CI's) and hypothesis tests: If the null hypothesis is rejected with significance level then the corresponding CI (see the table below) with confidence level does not contain the value targeted in the hypotheses, and vice versa. Therefore, it is often reasonable to present the CI suggested in the following table when the null hypothesis is rejected.

Hypothesis test | -level confidence interval |

Two-sided | |

One-sided with upper bound | |

One-sided with lower bound |