Test statistic

Definition

A test statistic is a standardized value that is calculated from sample data during a hypothesis test. It is used to determine whether to reject the null hypothesis.

5 Must Know Facts For Your Next Test

1. The test statistic for comparing two population means with known standard deviations often follows a normal distribution.
2. Commonly used test statistics in this context are the $z$-score.
3. The formula for the $z$-score in this context: $$ z = \frac{\bar{X}_1 - \bar{X}_2 - (\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}} $$
4. The value of the test statistic is compared against critical values from the standard normal distribution table.
5. If the absolute value of the test statistic exceeds the critical value, you reject the null hypothesis.

Review Questions

• What distribution does the test statistic follow when comparing two population means with known standard deviations?
• What is the formula for calculating the $z$-score in this context?
• When do you reject the null hypothesis based on the test statistic?

Related terms

Null Hypothesis: A statement that there is no effect or no difference, and it serves as a starting point for statistical testing.

$p$-value: The probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true.

$z$-score: $z$-scores measure how many standard deviations an element is from the mean; used here to compare sample means.