How can we use data to test a claim about a single population parameter?

The purpose of a hypothesis test is to use sample data to test a claim about a population parameter. Here are some research questions that could be answered by doing a hypothesis test:

Do the majority of community college students qualify for federal student loans? (hypothesis test for one proportion)

Has the average birth weight in a town decreased from 3500 grams? (hypothesis test for one mean)

From the claim, we state an assumption about the value of the population parameter. Could the data have come from this population? Or is the sample proportion (or sample mean) too far off? It depends on how much random samples from this population vary. We make a judgment about whether the sample proportion (or sample mean) is likely or unlikely to occur based on a sampling distribution for the parameter. If the data supports our claim and is unlikely, then we doubt our assumption about the population proportion (or population mean).

We can modify our Big Picture diagram to see how hypothesis testing is related to work we have done in previous modules.