AP Statistics Flashcards: Setting Up 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 10 cards to help you master important concepts.
Define the null hypothesis for a test comparing the means of two populations, μ1 and μ2.
The null hypothesis (H0) states there is no difference between the two population means, expressed as H0: μ1 - μ2 = 0 or H0: μ1 = μ2.
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Define the null hypothesis for a test comparing the means of two populations, μ1 and μ2.
The null hypothesis (H0) states there is no difference between the two population means, expressed as H0: μ1 - μ2 = 0 or H0: μ1 = μ2.
Before running a two-sample t-test to see if a new fertilizer (μ1) grows taller plants than an old one (μ2), what would the null hypothesis (H0) be?
The null hypothesis would be H0: μ1 - μ2 = 0 or H0: μ1 = μ2, assuming there is no difference in average plant height between the two fertilizers.
What are the two main conditions that must be verified before conducting a significance test for the difference of two population means?
The two main conditions to check are the independence of the samples and that the sampling distribution is approximately normal.
A student is comparing the mean battery life of two brands of smartphones. What two statistical assumptions must they check before proceeding with their test?
They must check for the independence of the two samples and verify that the sampling distribution of the difference in means is approximately normal.
Why is it necessary to verify conditions before performing a significance test for the difference of two population means?
Verifying conditions, such as independence and normality, ensures that the results and conclusions drawn from the two-sample t-test are valid.
What is the standard null hypothesis (H0) for a two-sample t-test for a difference of means?
The null hypothesis is H0: μ1 - μ2 = 0, which can also be written as H0: μ1 = μ2, indicating no difference between the population means.
What is the primary purpose of identifying the null and alternative hypotheses for a difference of two population means?
The purpose is to formally state the claim being tested, with the null hypothesis representing no difference and the alternative representing that a difference exists.
A researcher wants to compare the average test scores of two different teaching methods. What is the first step in setting up the appropriate significance test?
The first step is to identify the appropriate testing method, which is a two-sample t-test for the difference of two population means.
What is the appropriate statistical test for a difference of two population means?
The appropriate test for a difference of two population means is a two-sample t-test.
What is a two-sample t-test used for?
A two-sample t-test is the appropriate method used to test for a difference between two population means.