Methods and formulas for 1-Sample t

Select the method or formula of your choice.

Confidence interval (CI)

Formula

Notation

TermDescription
sample mean
t α/2 inverse cumulative probability of a t distribution with n-1 degrees of freedom at 1-α/2
α 1 – confidence level/100
s sample standard deviation
n sample size

T-value

Formula

Notation

TermDescription
sample mean
μ 0 hypothesized population mean
s sample standard deviation
n sample size

P-value

Formula

The calculation for the p-value depends on the alternative hypothesis.

Alternative Hypothesis P-value

Notation

TermDescription
μ population mean
μ0 hypothesized population mean
tt-statistic of the sample data
tn-1a random variable from the t-distribution with n-1 degrees of freedom
nsample size
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