AP Stats p-value interpretation cheat sheet

What does a p-value represent?

The probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true.

True or False: A lower p-value means stronger evidence against the null hypothesis.

True - A p-value less than the significance level suggests rejecting the null hypothesis.

Fill in the blank: A p-value of 0.05 indicates ______.

There is a 5% probability of observing the data if the null hypothesis is true.

How is a p-value used in hypothesis testing?

To determine whether to reject the null hypothesis based on a predetermined significance level (e.g., 0.05).

What happens if p < 0.01?

Strong evidence against the null hypothesis; often considered statistically significant.

Compare: p-value of 0.03 vs 0.07.

0.03 indicates stronger evidence against the null hypothesis than 0.07.

True or False: A p-value of 1.0 means the null hypothesis is true.

False - A p-value of 1.0 indicates no evidence against the null hypothesis.

Example: If p = 0.04, what can we conclude?

Since 0.04 < 0.05, we reject the null hypothesis and conclude significant results.

What is the significance level?

The threshold (e.g., 0.05) below which a p-value indicates significant results.

Effect of sample size on p-value?

Larger sample sizes yield smaller p-values for the same effect size, increasing significance.

If p = 0.08, what decision do we make?

We fail to reject the null hypothesis if our significance level is 0.05.

True or False: p-values can indicate the size of an effect.

False - p-values do not measure effect size; they only indicate significance.

What does p > 0.05 mean?

Insufficient evidence to reject the null hypothesis; results are not statistically significant.

Cause → Effect: High p-value.

Indicates weak evidence against the null hypothesis; no significant results.

What role does p-value play in Type I error?

A smaller p-value reduces the probability of a Type I error when rejecting the null hypothesis.

Example: Testing a new drug with p = 0.02.

We reject the null hypothesis and conclude the drug has a statistically significant effect.

A new marketing campaign costs $5000. p-value = 0.03. What does this mean?

There is a 3% probability of observing this result (or more extreme) if the null hypothesis is true. It suggests the campaign likely has a positive effect on sales.

True or False: A high p-value indicates strong evidence against the null hypothesis.

False. A high p-value suggests weak evidence against the null hypothesis; we fail to reject it.

Fill in the blank: If p-value < 0.05, we __________ the null hypothesis.

reject the null hypothesis.

Comparing two bike models, p-value = 0.15. Implication?

No significant difference in performance. The probability of observing this result under the null hypothesis is 15%.

If a store's average daily sales are $\displaystyle 2000, but a new strategy results in$2200 with p-value = 0.01, what to conclude?

With a 1% probability of this result occurring by chance, we reject the null. The strategy likely works.

A study shows average commute time is 30 min. New route averages 28 min, p-value = 0.04. Conclusion?

There’s a 4% chance of observing this difference due to random variation. We reject the null; the new route is faster.

What is the implication of a p-value of 0.10 in a rent increase study?

There’s a 10% chance of observing this rent increase under the null hypothesis; not statistically significant at the 0.05 level.

A clinical trial results in p-value = 0.002. What does this indicate?

Only a 0.2% chance of observing the results if the null hypothesis is true. Strong evidence for a treatment effect.