Questions and Answers
What is the formal procedure for using observed data to decide between two competing claims?
What is the null hypothesis?
The claim that we weigh evidence against in a significance test (statement of 'no difference').
What is the alternative hypothesis?
The claim that we are trying to find evidence for, which is hoped or suspected to be true instead of the null hypothesis.
What does it mean if the alternative hypothesis is one-sided?
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What does it mean if the alternative hypothesis is two-sided?
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Hypotheses always refer to what?
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What is a p-value?
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Small p-values provide convincing evidence for the alternative hypothesis.
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Large p-values provide convincing evidence for the alternative hypothesis.
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What does it indicate when the alternative hypothesis is two-sided?
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What does it mean to reject Ho?
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What does it mean to fail to reject Ho?
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What is the significance level?
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If the p-value > alpha, we say that the result is 'statistically significant at the a=________ level'.
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What is the significance at the a=0.05 level typically expressed by?
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Study Notes
Significance Testing Overview
- A significance test is a formal procedure used to evaluate observed data against two competing claims regarding a parameter (population mean or proportion).
- The null hypothesis (Ho) represents the statement of "no difference" that is tested against.
- The alternative hypothesis (Ha) is the claim we seek evidence for, suggesting a difference from the null hypothesis.
Types of Hypotheses
- A one-sided (or one-tailed) alternative hypothesis indicates the parameter value is either greater than or less than the null value.
- A two-sided (or two-tailed) alternative hypothesis indicates the parameter is simply different from the null value (not equal).
- Hypotheses always pertain to the population rather than a specific sample.
p-Value Significance
- The p-value measures the strength of the evidence against Ho and in favor of Ha by representing the probability of obtaining results at least as extreme as the observed data if Ho is true.
- Small p-values indicate strong evidence for Ha, suggesting the result is unlikely to occur under Ho.
- Large p-values fail to provide strong evidence against Ho, indicating the observed result is probable under Ho.
Evidence and Decision Making
- For a two-sided Ha, both values lower and higher than the null value contribute as evidence for Ha.
- Rejecting Ho occurs when the observed result is unlikely under Ho (indicated by a small p-value).
- Failing to reject Ho suggests that the observed result is likely by chance (indicated by a large p-value).
Significance Level
- The significance level (alpha) sets the threshold for determining statistical significance, indicating boundaries for results that are unlikely to happen by chance under Ho.
- A result is described as statistically significant at the alpha level when the p-value is less than alpha.
- Commonly, significance at the alpha = 0.05 level is expressed simply by stating "the results were significant (p < 0.05)."
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Description
Test your knowledge of key terms in AP Statistics Chapter 9.1. This quiz focuses on significance tests, the null hypothesis, and the alternative hypothesis, providing definitions and context for each term. Perfect for students preparing for exams or needing a quick review of statistical concepts.
