AP Statistics Flashcards: Concluding a Test for a Population Proportion
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 21 cards to help you master important concepts.
A researcher's conclusion is: "Because the p-value of 0.01 is less than α = 0.05, we reject H0. There is sufficient evidence that the new drug is effective." What key component is included here?
This conclusion correctly states the decision about the null hypothesis and provides the interpretation about the alternative hypothesis in context.
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A researcher's conclusion is: "Because the p-value of 0.01 is less than α = 0.05, we reject H0. There is sufficient evidence that the new drug is effective." What key component is included here?
This conclusion correctly states the decision about the null hypothesis and provides the interpretation about the alternative hypothesis in context.
Type I Error
A Type I error occurs when we reject a true null hypothesis. The probability of a Type I error is predetermined as the significance level, alpha (α).
Why is it incorrect to state "we accept H0" after a significance test?
This is incorrect because a significance test can never prove H0 is true; it can only determine if there is sufficient evidence for Ha.
How must the final conclusion about the alternative hypothesis be stated?
The conclusion about the alternative hypothesis must always be stated in the context of the research question.
To justify a claim about a population proportion, what two values must be compared?
To justify a claim, the calculated p-value from the test must be compared to the predetermined significance level, alpha (α).
After a test, you fail to reject H0. How do you justify your claim about the population?
You justify the claim by stating that because the p-value was greater than alpha, there is insufficient evidence to conclude the alternative hypothesis is true in context.
What does a large p-value imply about the null hypothesis?
A large p-value does not prove the null hypothesis is true; it only means we lack convincing evidence against it in favor of the alternative.
What is the formal decision rule for a significance test based on the p-value and alpha (α)?
If the p-value is less than or equal to alpha (p-value ≤ α), we reject the null hypothesis (H0). If the p-value is greater than alpha (p-value > α), we fail to reject the null hypothesis (H0).
What is the significance level, alpha (α)?
The significance level, alpha, is the predetermined probability of making a Type I error.
If a significance test results in a p-value of 0.21 with a significance level of α = 0.10, what is the correct decision?
Since the p-value (0.21) is greater than alpha (0.10), the correct decision is to fail to reject the null hypothesis (H0).
What are the two possible outcomes of a formal decision in a significance test?
The two possible outcomes are to either reject the null hypothesis (H0) or fail to reject the null hypothesis (H0).
What does it mean to reject the null hypothesis (H0) in terms of evidence?
Rejecting the null hypothesis (H0) means there is sufficient evidence to support the alternative hypothesis (Ha).
If a significance test for a population proportion yields a p-value of 0.04 and the significance level is α = 0.05, what is the correct decision?
Since the p-value (0.04) is less than or equal to alpha (0.05), the correct decision is to reject the null hypothesis (H0).
Can a significance test ever prove the null hypothesis is true?
No, a significance test can never prove that the null hypothesis (H0) is true.
What are the two essential parts of a complete conclusion for a significance test?
A complete conclusion includes the formal decision (reject or fail to reject H0) based on the p-value and alpha, and a statement about the alternative hypothesis in context.
What do large p-values indicate about the evidence for the alternative hypothesis?
Large p-values do not provide convincing evidence for the alternative hypothesis (Ha).
What is the ultimate purpose of conducting a significance test and analyzing its results?
The results of a significance test provide statistical reasoning to support an answer to a research question.
What does it mean to fail to reject the null hypothesis (H0) in terms of evidence?
Failing to reject the null hypothesis (H0) means there is insufficient evidence to support the alternative hypothesis (Ha).
What is the relationship between a p-value and the evidence for the alternative hypothesis (Ha)?
The smaller the p-value, the stronger the evidence for the alternative hypothesis (Ha).
What do small p-values indicate?
Small p-values provide evidence for the alternative hypothesis (Ha).
Statistical Reasoning (in context of significance tests)
Statistical reasoning is the justification for a conclusion about a research question that is based on the results of a significance test.