AP Stats Chapter 9: Testing a Claim

If we reject the null hypothesis when it is actually true, we commit a Type 1 ____

What is the probability that a significance test will reject the null when a particular alternative value of the parameter is true?

If we calculate a very small P value, we have evidence to ___ the null

Hypotheses always refer to the ____

The ___ hypothesis is the claim about the population for which we are finding evidence for

The test ____ is a standardized value that assesses how far the estimate is from the hypothesized parameter

Reject the null hypothesis if the P value is ___ than the significance level

What is the probability that we would observe a statistic at least as extreme as the one observed, assuming the null is true?

We can use a ___ test to compare observed data with a hypothesis about a population

If our calculated P value is not small enough to provide convincing evidence, we ___ to reject the null

Conclusions should always be written in ____

What is the Greek letter used to designate the significance level?

A ___ test allows us to analyze differences in responses within pairs

The ___ hypothesis is the claim for which we are seeking evidence against

An observed difference that is too small to have occurred due to chance alone is considered statistically ____

What are the statements a statistical test is designed to compare?

Key Concepts in Hypothesis Testing

Type 1 Error: Occurs when the null hypothesis is rejected while it is actually true.
Power of a Test: The likelihood that a significance test will correctly reject the null hypothesis for a specific alternative value.
Rejecting the Null: A very small P value provides evidence to reject the null hypothesis.
Population: All hypotheses refer to this overarching group considered in statistical analysis.

Hypothesis Definitions

Alternative Hypothesis: Represents the claim about the population for which evidence is being sought.
Test Statistic: A standardized measure that evaluates how far an estimate deviates from the hypothesized parameter.
P Value: Reflects the probability of observing a statistic as extreme as the one found, assuming the null hypothesis is true.

Decision Making in Hypothesis Testing

Significance Level (Alpha): The threshold for rejecting the null hypothesis, often denoted by the Greek letter alpha.
Comparison of P Value and Alpha: Reject the null hypothesis if the P value is less than the significance level.
Fail to Reject the Null: If the P value is not sufficiently small, there is not enough evidence to reject the null hypothesis.

Reporting Results

Contextual Conclusions: It's crucial to present conclusions within the appropriate context of the research.
Statistical Significance: An observed difference that is unlikely to be due to random chance is labeled as statistically significant.
Paired Tests: Designed to analyze differences in responses within defined pairs of observations.

Conclusion

Hypotheses: The competing statements that a statistical test is structured to evaluate.

This quiz covers key terms and concepts from Chapter 9 of AP Statistics, focusing on hypothesis testing and associated terminology. Flashcards include definitions for terms such as Type 1 error, power, and the process of rejecting the null hypothesis. Perfect for mastering statistical tests and their implications.