AP Statistics Flashcards: Carrying Out a Test for the Difference of Two Population Proportions
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 11 cards to help you master important concepts.
If you fail to reject the null hypothesis, what does this mean in the context of the two populations?
Failing to reject the null hypothesis means there is not enough statistical evidence to justify a claim that the two population proportions are different.
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If you fail to reject the null hypothesis, what does this mean in the context of the two populations?
Failing to reject the null hypothesis means there is not enough statistical evidence to justify a claim that the two population proportions are different.
What is the primary goal when you calculate a test statistic for the difference of two population proportions?
The goal is to determine how many standard deviations the observed difference in sample proportions is from the hypothesized difference of zero.
How do you make a formal decision about the null hypothesis using the p-value?
A formal decision is made by comparing the p-value to the significance level (alpha); you reject the null hypothesis if the p-value is less than or equal to alpha.
What type of test statistic is calculated for a difference of two population proportions?
The test statistic is a z-statistic that is calculated using the combined (pooled) proportion from both samples.
After conducting a test and finding a statistically significant result, how do you justify your claim?
You justify the claim by stating that because the p-value was less than the significance level, you reject the null hypothesis and have evidence for a difference in proportions.
In the context of a two-proportion test, what does the p-value represent?
The p-value is the probability of getting a difference in sample proportions as or more extreme than the observed difference, assuming the population proportions are equal.
What is the null hypothesis for a significance test for a difference of two population proportions?
The null hypothesis states that the two population proportions are equal (p₁ = p₂) or that their difference is zero (p₁ - p₂ = 0).
What are the two possible formal decisions you can make at the end of a significance test?
Based on the comparison of the p-value to alpha, the two possible decisions are to either reject the null hypothesis or fail to reject the null hypothesis.
What is the key assumption made when interpreting the p-value in a test for the difference of two population proportions?
The interpretation of a p-value assumes that the null hypothesis is true, meaning the two population proportions are assumed to be equal.
What is the purpose of calculating a combined (pooled) proportion?
The combined (pooled) proportion is used specifically to calculate the z-statistic for a significance test of a difference in proportions.
How do the results of a significance test for a difference of proportions relate to a research question?
The results provide the statistical reasoning needed to justify a claim and answer a research question about the difference between two population proportions.