Questions and Answers
What is a Significance Test?
What is the Null Hypothesis?
Claim tested by a statistical test
What does the Alternative Hypothesis claim?
Claim about the population that we are trying to find evidence for
A One-Sided Alternative hypothesis states that a parameter is larger than the null hypothesis value.
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A Two-Sided Alternative hypothesis is applicable when the parameter is claimed to be either larger or smaller than the null hypothesis value.
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What is a p-value?
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What is the significance level?
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What is a One-Sample Z Test?
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What does the Test Statistic measure?
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What is the One Sample T Test used for?
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What is Paired Data?
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What is the Four-Step Process in statistical testing?
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A result is statistically significant if the p-value is greater than the significance level.
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What is a Type I Error?
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What is a Type II Error?
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What does 'Power' represent in statistical testing?
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What are Degrees of Freedom?
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What is a T-Distribution?
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Study Notes
Statistical Tests and Hypotheses
- A Significance Test compares observed data against a claim or hypothesis.
- The Null Hypothesis represents a claim that is being tested statistically.
- Alternative Hypotheses support claims about the population, seeking evidence against the null.
Types of Alternatives
- One-Sided Alternative indicates a parameter is either larger or smaller than the null hypothesis value.
- Two-Sided Alternative suggests a parameter is different (either larger or smaller) from the null hypothesis value.
p-values and Significance
- A p-value measures the probability of obtaining a statistic as extreme as observed, under the null hypothesis.
- Statistical significance occurs when the p-value is less than the chosen significance level (α).
Test Types
- A One-Sample Z Test utilizes a simple random sample (SRS) from a large population with an unknown proportion of successes.
- A One Sample T Test assesses whether a sample’s mean suggests it originates from a specific population or a different one.
- Paired Data analysis involves obtaining two observations from either the same individual or from two similar individuals.
Error Types
- A Type I Error happens when the null hypothesis (H0) is rejected when it is actually true.
- A Type II Error occurs when failing to reject H0 when it is false.
Test Performance and Design
- The power of a test evaluates the probability of rejecting H0 at significance level α when a specified alternative is true.
- Degrees of Freedom is calculated as the number of independent observations minus the number of parameters estimated from the sample.
Distributions and Procedures
- The T-Distribution is a theoretical probability distribution used in hypothesis testing.
- Paired T Procedures involve statistical methods applied to paired samples for comparative analysis.
Significance Level and Testing
- The Significance Level reflects the probability of falsely rejecting the null hypothesis in a statistical test.
- The Four-Step Process for significance testing includes stating the hypotheses, planning the test, conducting it, and concluding the results.
General Concepts
- Statistically significant results provide evidence against the null hypothesis, helping in decision-making based on sample data.
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Description
Test your knowledge of key vocabulary from Chapter 9 of AP Statistics. This set of flashcards covers essential terms such as significance test, null hypothesis, and alternative hypotheses, helping you to understand statistical concepts effectively. Use these flashcards to prepare for your exams or reinforce your learning.