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Questions and Answers
What is a null hypothesis H0?
What is a null hypothesis H0?
A working hypothesis making a claim about the population parameter in question.
What is an alternate hypothesis H1?
What is an alternate hypothesis H1?
Any hypothesis that differs from the original claim being made.
What is a type I error?
What is a type I error?
Type I error is rejecting the null hypothesis when it is true.
What is a type II error?
What is a type II error?
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What is the level of significance of a test?
What is the level of significance of a test?
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What is the probability of a type II error?
What is the probability of a type II error?
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In a statistical test, which hypothesis determines the type of test used?
In a statistical test, which hypothesis determines the type of test used?
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If we fail to reject the null hypothesis, does this mean we have proved it to be true beyond all doubt?
If we fail to reject the null hypothesis, does this mean we have proved it to be true beyond all doubt?
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If we reject the null hypothesis, does this mean we have proved it to be false beyond all doubt?
If we reject the null hypothesis, does this mean we have proved it to be false beyond all doubt?
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To test μ for an x distribution that is mound-shaped using sample size n ≥ 30, when do you use the normal distribution vs. Student's t distribution?
To test μ for an x distribution that is mound-shaped using sample size n ≥ 30, when do you use the normal distribution vs. Student's t distribution?
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When using the Student's t distribution to test μ, what value do you use for the degrees of freedom?
When using the Student's t distribution to test μ, what value do you use for the degrees of freedom?
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If the P-value allows you to reject H0 at the 5% level of significance, can you always reject H0 at the 1% level?
If the P-value allows you to reject H0 at the 5% level of significance, can you always reject H0 at the 1% level?
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If the P-value allows you to reject H0 for α = .01, can you always reject H0 for α = .05?
If the P-value allows you to reject H0 for α = .01, can you always reject H0 for α = .05?
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To use the normal distribution to test a proportion p, do the values come from H0 or are they estimated using p̂ from the sample?
To use the normal distribution to test a proportion p, do the values come from H0 or are they estimated using p̂ from the sample?
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What do we mean when we say a test is significant? Does this necessarily mean the results are important?
What do we mean when we say a test is significant? Does this necessarily mean the results are important?
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Study Notes
Hypotheses
- Null hypothesis (H0): A claim about a population parameter that is subject to testing.
- Alternate hypothesis (H1): Any hypothesis that opposes the claim of the null hypothesis.
Errors in Hypothesis Testing
- Type I error: Mistaken rejection of a true null hypothesis; represents a false positive.
- Type II error: Failure to reject a false null hypothesis; represents a false negative.
Significance Levels
- Level of significance: The probability of committing a Type I error during hypothesis testing.
- Probability of Type II error: Represented by the symbol beta (β).
Test Types and Decisions
- Selection of test type (left-tailed, right-tailed, two-tailed) is based on the alternative hypothesis, which defines the area of interest in the parameter space.
- Failure to reject H0 does not confirm its truth; it indicates insufficient evidence to dismiss it.
Implications of Rejecting Hypotheses
- Rejecting H0 does not guarantee its falsehood; there remains a risk of a Type I error.
Distribution Choices
- For a mound-shaped distribution (n ≥ 30):
- Use standard normal distribution if population standard deviation (σ) is known.
- Use Student's t distribution with n - 1 degrees of freedom if σ is unknown.
Degrees of Freedom
- In Student's t distribution, degrees of freedom are calculated as n - 1.
P-Value Interpretations
- If the P-value allows rejection of H0 at the 5% significance level, it may not allow rejection at the 1% level if it falls between 0.01 and 0.05.
- A P-value that permits rejection at α = 0.01 will always allow rejection at α = 0.05 due to the nested nature of significance levels.
Proportional Testing Conditions
- Normal distribution testing of proportion p requires that conditions np > 5 and nq > 5 are satisfied.
- The value of p used is derived from the null hypothesis (H0), not estimated from the sample proportion (p̂).
Significance vs Practical Importance
- A test is deemed significant if the null hypothesis is rejected; however, this does not inherently indicate the practical relevance of the findings.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of key concepts from Statistics Chapter 9 with these flashcards. This quiz covers hypotheses, type I and type II errors, and critical statistical terms. Great for students looking to reinforce their understanding before exams.
