Target: To check if the assumed μ_{0} is statistically correct, based on a sample average and sample standard deviation

Example1: A farmer calculated last year the average of the apples' weight in his apple orchard μ_{0} equals 17 kg, based on big sample

Current year he checked a small sample of apples and the sample average x equals 18 kg

Was the average of the apple's weight changed this year?

The population's distribution is Normal | |

The standard deviations of the population is unknown | |

Population expected mean is known |

Sample average of the population | |

Sample standard deviation of the population | |

Sample size of the population |

Hypotheses

H

If you enter raw data, the tool will run the Shapiro-Wilk normality test and calculate outliers, as part of the test calculation.

or
or enter summarized data (x, n, μ_{0}, S) in Group form

**Header**:
You may change groups' name to the real names.

**Data**:
When entering data, press Enter after each value

You may copy data from Excel, Google sheets or any tool that separate data with **Tab** and **Line Feed**.

Copy the data, **one column includes the header**, and paste below.

x: | Sample average | |

μ_{0}: |
Assumed population mean | |

n: | Sample size | |

S: | Sample standard deviation | |

skewness: | ||

Normality pval: | Shapiro Wilk test | |

Outliers | count: ,based on the Tukey's fences method, k=1.5 |

validateion message