Target: To check if the assumed σ^{2}_{0} is statistically correct, based on a sample varaince S^{2}

Example1: A farmer calculated last year the varaince of the apples' weight in his apple orchard σ^{2}_{0} equals 2 kg^{2}, based on big sample Current year he checked a small sample of apples and the sample varaince S^{2} equals 3 kg^{2} Was the variance of the apple's weight changed this year?

Assumptions

The population's distribution is Normal

You assume you know the population variance ( σ^{2}=σ^{2}_{0})

Required Sample Data

Sample variance of the population

Sample size of the population

Enter input data and then press "Calculate test" button to get the results

Hypotheses

H_{0}: σ^{2} ≥ σ^{2}_{0}

H_{0}: σ^{2} = σ^{2}_{0}

H_{0}: σ^{2} ≤ σ^{2}_{0}

H_{1}: σ^{2} < σ^{2}_{0}

H_{1}: σ^{2} ≠ σ^{2}_{0}

H_{1}: σ^{2} > σ^{2}_{0}

Test statistic

χ² distribution

Test calculation

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

tails: the default is right tailed test (usually you worried only if the standard deviation is bigger then the expected one)

Statistic Data

oror enter summarized data (x, n, σ, S) in Group form

Enter sample data

Header: You may change groups' name to the real names. Data: When entering data, press Enter after each value

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

Enter sample data

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.

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