Wiki Page, Math 13 - Perez Sandbox : ANSWER(S): Module 20 - Introduction to Hypothesis Testing (4a of 5 discussion 1)

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2026-01-17T21:14:50-08:00

In general, the P-value is the probability that sample results are as extreme, or more extreme, than the result observed in the data, if the null hypothesis is true. The phrase “as extreme or more extreme” means further from the center of the sampling distribution in the direction of the alternative hypothesis.

We need to say this in the context of the opinion that reducing health care costs is a national priority. In the random sample of 1505 U.S. adults, 70% had this view this year. The null hypothesis is that 68% of all U.S. adults have this view this year. The P-value is 0.045.

What does the 0.045 mean?

This P-value tells us that there is a 4.5% chance that in a random sample of 1,505 U.S. adults, 70% or more will have the view that reducing health care costs is a national priority if in reality 68% of the population has this opinion.

Here is another way to explain it:

If 68% of the population of U.S. adults think that reducing health care costs is a national priority, then how likely is it that a random sample of 1505 U.S. adults will have 70% or more with this opinion? The probability is 0.045 = 4.5%.