Chapter 8: Hypothesis Tests for One Population

A statistic is a characteristic or measure from a sample. A parameter is a characteristic or measure from a population. We use statistics to generalize about parameters, known as estimations. Every time we take a sample statistic, we would expect that estimate to be close to the parameter, but not necessarily exactly equal to the unknown population parameter. How close would depend on how large a sample we took, who was sampled, how they were sampled and other factors. Hypothesis testing is a scientific method used to evaluate claims about population parameters.

A statistical hypothesis is an educated conjecture about a population parameter. This conjecture may or may not be true. We will take sample data and infer from the sample if there is evidence to support our claim about the unknown population parameter.

The null hypothesis (H₀, pronounced “H-naught” or “H-zero”), is a statistical hypothesis that states that there is no difference between a parameter and a specific value, or that there is no difference between two parameters. The null hypothesis is assumed true until there is sufficient evidence otherwise.

The alternative hypothesis (H₁ or H_a, pronounced “H-one” or “H-ā”), is a statistical hypothesis that states that there is a difference between a parameter and a specific value, or that there is a difference between two parameters. H₁ is always the complement of H₀.

The researcher decides the probability that the test is true by setting the level of significance, also called the significance level. We use the Greek letter α, pronounced “alpha,” to represent the significance level. The level of significance is the probability that the null hypothesis is rejected when it is actually true. Note: like in the previous chapter, 1 – $\alpha$ is the confidence level.

When doing your own research, you should set up their hypotheses and choose the significance level before analyzing the sample data.

When reading a word problem, your first step is to identify the parameter(s), for example μ, you are testing and which direction (left, right, or two-tail) test you are being asked to perform. For this course, the homework problems will state the researcher’s claim; usually this is the alternative hypothesis.