# One Sample T-Test Calculator

## Unknown standard deviation

Target: To check if the assumed μ0 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 μ0 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?

## Assumptions

 The population's distribution is Normal The standard deviations of the population is unknown Population expected mean is known

## Required Sample Data

 Sample average of the population Sample standard deviation of the population Sample size of the population

## Hypotheses

H0: μ ≥ μ0 H0: μ = μ0 H0: μ ≤ μ0
H1: μ < μ0 H1: μ ≠ μ0 H1: μ > μ0

## 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.

### Statistic Data

 α: Significant level (0-1), maximum chance allowed rejecting H0 while H0 is correcrt (Type1 Error) Outliers: Included Excluded It is not recommended to exclude outliers unless you know the reasons
or or enter summarized data (x, n, μ0, 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

## 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

### Group:

 x: Sample average μ0: 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