Wiki Page, Math 13 - Perez Sandbox : Module 20 - Introduction to Hypothesis Testing (1b of 5)

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2026-01-17T21:15:29-08:00

Next Steps: Forming Hypotheses

We already know that in inference we use a sample to draw a conclusion about a population. If the research question contains a claim about the population, we translate the claim into two related hypotheses.

The null hypothesis states the value of the parameter that we assume to be true about the population. The null hypothesis is abbreviated .

The alternative hypothesis reflects the claim in the research question about the parameter. The alternative hypothesis says the parameter is “greater than” or “less than” or “not equal to” the value we assume to true in the null hypothesis. The alternative hypothesis is abbreviated .

EXAMPLE Stating hypotheses from a research question

Is the average course load for community college students less than 12 semester hours?

: The mean course load for community college students is equal to 12 semester hours.

: The mean course load for community college students is less than 12 semester hours.

Do the majority of community college students qualify for federal student loans?

: The proportion of community college students who qualify for federal student loans is 0.5.

: The proportion of community college students who qualify for federal student loans is greater than 0.5.

When the research question contains a claim that compares two populations, the null hypothesis states that the parameters are equal, which is equivalent to saying that there is “no difference” in parameter values.

In community colleges, do female students and male students have different mean GPAs?

: In community colleges, female and male students have the same mean GPAs.

: In community colleges, female and male students have different mean GPAs.

Are college athletes more likely than non-athletes to receive academic advising?

: In colleges, the proportion of athletes who receive academic advising is equal to the proportion of non-athletes who receive academic advising.

: In colleges, the proportion of athletes who receive academic advising is greater than the proportion of non-athletes who receive academic advising.

Comment

Here are some general observations about null and alternative hypotheses.

Both hypotheses are statements about the same population parameter or same two population parameters.

The null hypothesis always contains an equal sign.

The alternative hypothesis is always an inequality statement. It contains a “less than” or a “greater than” or a “not equal to” symbol.

In a statistical investigation, we determine the research question, and thus the hypotheses, before we collect data. The process of forming hypotheses, collecting data, and using the data to draw a conclusion about the hypotheses is called hypothesis testing.

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