A null hypothesis (H0) is the default assumption that there is no significant relationship or effect between variables. In hypothesis testing, you attempt to reject the null hypothesis using your sample data. If your p-value falls below your significance level (typically 0.05), you reject the null.

A p-value of 0.03 means there is a 3% probability of observing your results (or more extreme results) if the null hypothesis were true. Since 0.03 < 0.05, you would reject the null hypothesis at the 5% significance level and conclude the result is statistically significant.

A Type I error (false positive) occurs when you reject a true null hypothesis. A Type II error (false negative) occurs when you fail to reject a false null hypothesis. The probability of a Type I error equals your significance level alpha, while the probability of a Type II error is called beta.

Use a z-test when your sample size is large (n > 30) and the population standard deviation is known. Use a t-test when your sample size is small (n ? 30) or when the population standard deviation is unknown and you are using the sample standard deviation instead.

Statistical power is the probability that a test will correctly reject a false null hypothesis (i.e., detect a real effect when it exists). Power equals 1 minus beta. Researchers typically aim for 80% power. Power increases with larger sample sizes, larger effect sizes, and higher significance levels.