About the null and alternative hypotheses

The null and alternative hypotheses are two mutually exclusive statements about a population. A hypothesis test uses sample data to determine whether to reject the null hypothesis.

Null hypothesis (H₀): The null hypothesis states that a population parameter (such as the mean, the standard deviation, and so on) is equal to a hypothesized value. The null hypothesis is often an initial claim that is based on previous analyses or specialized knowledge.
Alternative Hypothesis (H₁): The alternative hypothesis states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis. The alternative hypothesis is what you might believe to be true or hope to prove true.

One-sided and two-sided hypotheses

The alternative hypothesis can be either one-sided or two sided.

Two-sided: Use a two-sided alternative hypothesis (also known as a nondirectional hypothesis) to determine whether the population parameter is either greater than or less than the hypothesized value. A two-sided test can detect when the population parameter differs in either direction, but has less power than a one-sided test.
One-sided: Use a one-sided alternative hypothesis (also known as a directional hypothesis) to determine whether the population parameter differs from the hypothesized value in a specific direction. You can specify the direction to be either greater than or less than the hypothesized value. A one-sided test has greater power than a two-sided test, but it cannot detect whether the population parameter differs in the opposite direction.

Examples of two-sided and one-sided hypotheses

Two-sided: A researcher has results for a sample of students who took a national exam at a high school. The researcher wants to know if the scores at that school differ from the national average of 850. A two-sided alternative hypothesis (also known as a nondirectional hypothesis) is appropriate because the researcher is interested in determining whether the scores are either less than or greater than the national average. (H₀: μ = 850 vs. H₁: μ≠ 850)
One-sided: A researcher has exam results for a sample of students who took a training course for a national exam. The researcher wants to know if trained students score above the national average of 850. A one-sided alternative hypothesis (also known as a directional hypothesis) can be used because the researcher is specifically hypothesizing that scores for trained students are greater than the national average. (H₀: μ = 850 vs. H₁: μ > 850)