Hypothesis Test Simulator

Simulate a one-sample z test and p-value decision

Sample mean

Null mean

Std dev

Alternative

Z Test Formulas

Standard error	SE = sigma / sqrt(n)
Z statistic	z = (xbar - mu0) / SE
Decision rule	reject H0 if p-value < alpha

Step-by-Step Example

If xbar = 105, mu0 = 100, sigma = 15, and n = 36, then SE = 15 / sqrt(36) = 2.5. The z statistic is (105 - 100) / 2.5 = 2. A two-sided test gives a p-value of about 0.0455.

Common Mistakes

Interpreting p-value as the probability that the null hypothesis is true.
Choosing the alternative direction after seeing the data.
Ignoring assumptions about independence and sampling.
Confusing statistical significance with practical importance.

Frequently Asked Questions

What is a hypothesis test?▼

A hypothesis test uses sample data to evaluate whether evidence is strong enough against a null hypothesis.

What is a p-value?▼

A p-value is the probability of seeing a result at least as extreme as the observed result if the null hypothesis is true.

What is a z statistic?▼

A z statistic measures how many standard errors the sample mean is from the hypothesized mean.

When do you reject the null hypothesis?▼

A common rule is to reject the null hypothesis when the p-value is less than the significance level alpha.

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