Statistics Chapter 9 Test Flashcards

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Questions and Answers

What is a null hypothesis H0?

A working hypothesis making a claim about the population parameter in question.

What is an alternate hypothesis H1?

Any hypothesis that differs from the original claim being made.

What is a type I error?

Type I error is rejecting the null hypothesis when it is true.

What is a type II error?

Type II error is failing to reject the null hypothesis when it is false. Signup and view all the answers

What is the level of significance of a test?

The probability of a type I error. Signup and view all the answers

What is the probability of a type II error?

beta Signup and view all the answers

In a statistical test, which hypothesis determines the type of test used?

The alternative hypothesis. Signup and view all the answers

If we fail to reject the null hypothesis, does this mean we have proved it to be true beyond all doubt?

No, it suggests that the evidence is not sufficient to merit rejecting the null hypothesis. Signup and view all the answers

If we reject the null hypothesis, does this mean we have proved it to be false beyond all doubt?

No, the test was conducted with a risk of a type I error. Signup and view all the answers

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?

If (sigma) is known, use the normal distribution. If (sigma) is unknown, use the Student's t distribution with n-1 degrees of freedom. Signup and view all the answers

When using the Student's t distribution to test μ, what value do you use for the degrees of freedom?

n-1 Signup and view all the answers

If the P-value allows you to reject H0 at the 5% level of significance, can you always reject H0 at the 1% level?

No, if the P-value lies between 0.01 and 0.05 you would reject at the 5% level, but not at the 1% level. Signup and view all the answers

If the P-value allows you to reject H0 for α = .01, can you always reject H0 for α = .05?

Yes, if H0 is rejected at the 1% level it will always be rejected at the 5% level. Signup and view all the answers

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?

The value of (p_rho) comes from H0. Signup and view all the answers

What do we mean when we say a test is significant? Does this necessarily mean the results are important?

A significant test means we reject the null hypothesis. This does not necessarily imply that the results are practically significant. Signup and view all the answers

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.

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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.