AP Statistics Flashcards: Setting Up a Test for a Population Mean
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 14 cards to help you master important concepts.
What is the appropriate testing method for a population mean when the population standard deviation (sigma) is unknown?
The appropriate test for a population mean with an unknown sigma is a one-sample t-test.
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What is the appropriate testing method for a population mean when the population standard deviation (sigma) is unknown?
The appropriate test for a population mean with an unknown sigma is a one-sample t-test.
What two conditions for inference must be verified before performing a one-sample t-test for a population mean?
The two conditions that must be verified are the independence condition and the condition that the sampling distribution of the mean is approximately normal.
What is the standard form of the null hypothesis for a one-sample t-test?
The null hypothesis for a one-sample t-test is H0: mu = mu0, where mu0 is the hypothesized value of the population mean.
What two main conditions must be verified to conduct a test for a population mean?
To test a population mean, you must check for independence of the data and verify that the sampling distribution is approximately normal.
What is the primary data transformation required before conducting a matched pairs t-test?
The primary transformation is to calculate the difference between each pair of observations, creating a single sample of differences.
Alternative Hypothesis (Ha) for a population mean
The alternative hypothesis proposes that the population mean is actually less than, greater than, or simply not equal to the value stated in the null hypothesis.
Null Hypothesis (H0) for a population mean
The null hypothesis states that the true population mean (mu) is equal to a specified value (mu0).
When setting up a matched pairs test, why is it important to define the order of subtraction?
It is important to define the order of subtraction for the mean difference to ensure the correct interpretation of the parameter and the direction of the alternative hypothesis.
One-sample t-test for a population mean
This is the appropriate testing method to use for a single population mean when the population standard deviation (sigma) is not known.
How can matched pairs data be analyzed when testing a hypothesis about a population mean?
Matched pairs data can be analyzed with a one-sample t-test performed on the calculated differences between the pairs.
To test if a training program increases productivity, you measure output before and after for each worker. How would you define your parameter and set up a one-sided null and alternative hypothesis?
Define μ_diff = (output after - output before). The hypotheses would be H0: μ_diff = 0 and Ha: μ_diff > 0.
A researcher measures the blood pressure of 25 individuals before and after a new medication. What statistical test is appropriate for this data if sigma is unknown?
A one-sample t-test on the differences in blood pressure should be used, as this is matched pairs data.
What is the parameter of interest in a matched pairs t-test?
The parameter of interest is the true mean of the differences (μ_diff) for the entire population of matched pairs.
A company claims its batteries last for an average of 500 hours. To test this claim with an unknown sigma, what would the null and alternative hypotheses be for a two-sided test?
The null hypothesis would be H0: mu = 500, and the alternative hypothesis would be Ha: mu ≠ 500.