AP Statistics Chapter 9 Test Flashcards

Questions and Answers

What does 'guilty' indicate in hypothesis testing?

p ≤ α → reject Ho → there is convincing evidence for Ha (in context) (correct)

p < α → evidence is inconclusive

p = α → neither reject nor accept Ho

p > α → fail to reject Ho → there is not convincing evidence for Ha (in context)

What does a p-value represent in hypothesis testing?

Assuming the true parameter, there is about a _p-value% probability that the sample resulted from Ha by chance alone.

What does the null hypothesis Ho: σ = 15 mean in the context of Mike testing a new 7-iron?

The true standard deviation with the new 7-iron is 15 yards.

Interpret the P-value of 0.25 in Mike's testing context.

Assuming the true standard deviation is 15 yards, there is about a 0.25 probability that the sample standard deviation would be 13.9 yards or less by chance alone. Signup and view all the answers

What is a Type I error in the context of the new deluxe AAA battery?

Finding convincing evidence that the new batteries last longer than 30 hours when in reality their true mean lifetime is 30 hours. Signup and view all the answers

What is a Type II error in the context of the new deluxe AAA battery?

Not finding convincing evidence that the new batteries last longer than 30 hours when in reality their true mean lifetime is greater than 30 hours. Signup and view all the answers

Which type of error is more serious in the context of the new deluxe AAA battery, and why?

The answer will vary, but a Type I error could lead the company to produce a product that is not better, while a Type II error could mean missing out on a superior product. Signup and view all the answers

What are the hypotheses for the company's new deluxe AAA batteries?

Ho: μ = 30 hours; Ha: μ > 30 hours Signup and view all the answers

What are the sample parameters used in the 1-PropZTest for battery life?

po = 0.8, x = 32, n = 50. Signup and view all the answers

Study Notes

Hypothesis Testing

A "guilty" finding corresponds to p ≤ α, leading to the rejection of the null hypothesis (Ho), indicating convincing evidence for the alternative hypothesis (Ha).
A "not guilty" finding corresponds to p > α, resulting in failing to reject Ho, signifying a lack of convincing evidence for Ha.

p-value Interpretation

A p-value expresses the probability of observing the sample data (or more extreme) assuming the null hypothesis is true.
It quantifies how likely the observed results could occur purely by chance.

Golf Test Case

Null hypothesis (Ho): The standard deviation of shots with the new 7-iron is 15 yards.
Alternative hypothesis (Ha): The standard deviation of shots with the new 7-iron is less than 15 yards.
Observed sample standard deviation is 13.9 yards from 50 shots.
A p-value of 0.25 indicates there is a 25% chance of observing a standard deviation of 13.9 yards or less if the true standard deviation is indeed 15 yards.

Types of Errors

Type I Error: Convicting an innocent person; finding significant evidence against the null hypothesis when it is true.
Type II Error: Letting a guilty person go free; failing to find significant evidence against the null hypothesis when it is false.

New AAA Battery Case

Null hypothesis (Ho): The mean lifetime of the new batteries is 30 hours.
Alternative hypothesis (Ha): The mean lifetime of the new batteries is greater than 30 hours.
Sample mean lifetime of the new batteries is 33.9 hours from 15 batteries.
The resulting p-value of 0.0729 indicates some evidence, but not strong enough to reject Ho.
Type I Error in this context: Incorrectly concluding that the new batteries last longer than 30 hours when they do not, potentially leading to unnecessary production costs.
Type II Error: Failing to recognize that the new batteries do last longer than 30 hours, which would result in missed opportunities for production.
The seriousness of the error may vary, but a Type I error could lead to financial losses while a Type II error could prevent the introduction of a better product.

Test Statistic Calculation

The calculation for testing proportions uses the 1-PropZTest, where:
- po (hypothesized proportion) = 0.8
- x (number of successes in the sample) = 32
- n (sample size) = 50.

Description

This quiz focuses on key concepts from Chapter 9 of the AP Statistics curriculum, including hypothesis testing and p-values. Each flashcard presents essential definitions and interpretations vital for mastering statistical inference. Enhance your understanding and prepare effectively for your assessments.