or or enter summarized data (x̅, n, σ, S) below

**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 block of 2 consecutive columns includes the header**, and paste below.

Copy the data,

It is okay to leave empty cells, empty cells or non numeric cells won't be counted

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

validation message

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

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?

Hypotheses

H_{0}: μ ≥ = ≤ μ_{0}

H_{1}: μ < ≠ > μ_{0}

Test statistic

Normal distribution

Normal distribution | |

The standard deviations of the population is known | |

Population expected mean is known |

Sample average | |

Sample size |

The following R code should produce the same results:

Currently, there is no direct R function for the one-sample z test.

__Examples__

1. Two-tailed test

A farmer calculated last year the average of the apples' weight in his apple orchard μ0 equals 17kg, based on a big sample.

The current year the sample average x̅ equals 16kg.

Was the average of the apple's weight in the entire orchard changed this year? or is it just a random difference?

2. Left tail test.

In the same example as above, the farmer only cares if the entire average is lesser this year.