AP Statistics Flashcards: Carrying Out a Test for the Difference of Two Population Means
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.
What is the shape of the sampling distribution for the t-statistic for a difference of two means?
The sampling distribution of the t-statistic for a difference of two means is an approximate t-distribution.
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What is the shape of the sampling distribution for the t-statistic for a difference of two means?
The sampling distribution of the t-statistic for a difference of two means is an approximate t-distribution.
If the p-value is larger than the significance level (α), what conclusion can be justified?
We fail to reject the null hypothesis and state that we do not have convincing evidence to justify a claim of a difference between the two population means.
How is a formal decision made in a significance test?
A formal decision is made by comparing the p-value to the significance level (alpha); if the p-value is less than or equal to alpha, we reject the null hypothesis.
Define the p-value in the context of a test for a difference of two population means.
The p-value is the probability of getting a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis (of no difference) is true.
A test comparing the mean effectiveness of two allergy medicines yields a p-value of 0.04. How is this p-value interpreted in context?
Assuming the two medicines have the same mean effectiveness, there is a 4% chance of observing a difference in sample means as large or larger than the one found in the study.
If the p-value is smaller than the significance level (α), what conclusion can be justified?
We reject the null hypothesis and can justify the claim that there is convincing evidence of a difference between the two population means.
What is the overall purpose of conducting a significance test for a difference of two means?
The purpose is to provide statistical reasoning, based on sample data, to support or reject a claim about a research question involving two populations.
What test statistic is calculated for a significance test for a difference of two population means?
An appropriate test statistic is a t-statistic, which measures how far the observed difference in sample means is from the hypothesized difference.
How are the degrees of freedom determined for a two-sample t-test?
The degrees of freedom for the approximate t-distribution are calculated using a complex formula that is best found by technology.
Using α = 0.05, what claim can be justified based on a p-value of 0.04 from a test for the difference of two means?
Since the p-value (0.04) is less than alpha (0.05), we can justify the claim that there is a statistically significant difference between the means of the two populations.
What fundamental assumption is made when interpreting a p-value?
The interpretation of a p-value for a test for a difference of means always assumes that the null hypothesis is true.