Summary of formulas

$H_o$ and $H_a$ are contradictory.

If $\alpha \le$ p-value, then do not reject $H_o$ .

If $\alpha >$ p-value, then reject $H_o$ .

$\alpha$ is preconceived. Its value is set before the hypothesis test starts.The p-value is calculated from the data.

$\alpha$ = probability of a Type I error = P(Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.

$\beta$ = probability of a Type II error = P(Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false.

If there is no given preconceived $\alpha$ , then use $\alpha =0.05$ .

Types of hypothesis tests

• Single population mean, known population variance (or standard deviation): Normal test .
• Single population mean, unknown population variance (or standard deviation): Student's-t test .
• Single population proportion: Normal test .