From BYU-I Statistics Text
- The null hypothesis ($H_0$) is the foundational assumption about a population and represents the status quo. It is a statement of equality ($=$). The alternative hypothesis ($H_a$) is a different assumption about a population and is a statement of inequality ($<$, $>$, or $\ne$). Using a hypothesis test, we determine whether it is more likely that the null hypothesis or the alternative hypothesis is true.
- The $P$-value is the probability of getting a test statistic at least as extreme as the one you got, assuming $H_0$ is true. A $P$-value is calculated by finding the area under the normal distribution curve that is more extreme (farther away from the mean) than the z-score. The alternative hypothesis tells us whether we look at both tails or only one.
- The level of significance ($\alpha$) is the standard for determining whether or not the null hypothesis should be rejected. Typical values for $\alpha$ are $0.05$, $0.10$, and $0.01$. If the $P$-value is less than $\alpha$ we reject the null. If the $P$-value is not less than $\alpha$ we fail to reject the null.
- A Type I error is committed when we reject a null hypothesis that is, in reality, true. A Type II error is committed when we fail to reject a null hypothesis that is, in reality, not true. The value of $\alpha$ is the probability of committing a Type I error.