One Sample T-Test Calculator

One Sample t-test is used to check whether the population mean is statistically significantly different from a hypothesized value. For example : Ideal cholesterol level should be below 200. With the use of one-sample t-test we can examine if the average cholestrol level of the population is statistically different from 200.

In the calculation below you have two options - either to enter raw data or you can enter summary information which is required to calculate one sample t-test. Under raw data tab, you can enter values separated by comma, space, tab spaces or new line.

Enter Raw Data

Paste data below from MS Excel or Notepad. Sample X Hypothesized population mean ( $\mu_{0}$ )

Enter Summary Data

Sample mean ( $\bar{x}$ ) Sample Standard Deviation (s) Sample Size (n) Hypothesized population mean ( $\mu_{0}$ )

Solution t = 0.270121
p-value (One-tailed) = 0.402292
p-value (Two-tailed) = 0.804584
Degree of freedom = 3
Population mean is not significantly different from a hypothesized value at 5% significance level(One-tailed)
Population mean is not significantly different from a hypothesized value at 5% significance level(Two-tailed)

Step by Step Calculation

$s_{\bar{x}} = \frac{s}{\sqrt{n}}$

$s_{\bar{x}} =\frac{55.5308}{\sqrt{4}}$
$s_{\bar{x}} =27.7654$
$t = \frac{\bar{x}-\mu{}_{0}}{s_{\bar{x}}}$
$t = \frac{317.5-310.0000}{27.7654}$ $t = 0.270121$

$\mu_{0}$ : Hypothesized value
$\bar{x}$ : Sample mean
$n$ : Sample size
$s$ : Sample standard deviation
$s_{\bar{x}}$ : Estimated standard error of the mean

Assumptions of One Sample t-test

Data must be normally distributed
Sample must be picked randomly from population
Data must be continuous