Methods and formulas for 1-Sample Z

Select the method or formula of your choice.

Confidence interval

Formula

Notation

TermDescription
sample mean
zα/2 inverse cumulative probability of the standard normal distribution at 1- α /2; α = 1 - confidence level/100
σ population standard deviation (assumed known)
n sample size

Z-value

Formula

Notation

TermDescription
sample mean
μ0 hypothesized population mean
σ population standard deviation (assumed known)
n sample size

P-value

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

Alternative Hypothesis P-value

Notation

TermDescription
μ population mean
μ0 hypothesized population mean
zz-value of the sample data
Z a random variable from the standard normal distribution
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