AP Stats Type I vs Type II errors review

Type I error

Rejecting the null hypothesis when it is actually true. Example: Concluding a new drug works when it doesn't.

Type II error

Failing to reject the null hypothesis when it is false. Example: Concluding a new drug doesn't work when it does.

True or False: Type I errors are more serious than Type II errors.

False. The seriousness depends on the context. E.g., a Type I error in medical trials can lead to unsafe drug approval.

If the significance level is lowered, what happens to Type I and Type II errors?

Type I errors decrease, Type II errors increase. Lowering alpha makes it harder to reject the null.

Examples of Type I error in retail.

Concluding a marketing campaign is effective when sales didn't actually increase. Loss of budget.

Examples of Type II error in travel.

Not booking a flight believing it's too expensive when it's discounted. Missing a good deal.

Fill in the blank: A Type I error is often referred to as a __________.

false positive. It indicates a test detected an effect that isn’t real.

Fill in the blank: A Type II error is often referred to as a __________.

false negative. It fails to detect a real effect.

Comparison: Type I error vs. Type II error.

Type I: false positive; Type II: false negative. One detects an effect that isn't real, the other misses a real effect.

Scenario: Testing a new coffee blend.

Type I: Conclude it tastes better when it doesn't. Type II: Conclude it doesn’t taste better when it does.

Calculate the impact: Lowering alpha from 0.05 to 0.01.

Type I errors decrease. Type II errors increase, meaning fewer true effects might be detected.

How do sample size and Type II error relate?

Larger sample sizes reduce Type II errors. They provide more power to detect a true effect.

True or False: Increasing sample size always reduces Type I errors.

False. Increasing sample size primarily affects Type II errors, not Type I errors directly.

Real-life consequence of Type I error in healthcare.

Wrongly diagnosing a patient with a disease, leading to unnecessary treatment and stress.

Type I error definition?

A Type I error occurs when we reject a true null hypothesis. Example: Concluding a new medication works when it actually doesn't.

Type II error definition?

A Type II error happens when we fail to reject a false null hypothesis. Example: Concluding a new medication does not work when it actually does.

True or False: Type I errors are more costly than Type II errors.

False. It depends on context. In medical trials, Type I errors (false positives) can lead to unnecessary treatments.

Fill in the blank: A Type I error is also called a ____ error.

False positive.

Fill in the blank: A Type II error is also called a ____ error.

False negative.

Comparison: Type I vs Type II errors.

- Type I: Rejecting true null - Type II: Failing to reject false null

Example of Type I error in a store.

A store claims a new marketing strategy increases sales, but actual sales remain unchanged.

Example of Type II error in a store.

A store fails to notice that a new promotion actually increases sales, leading to lost revenue.

What increases chance of Type I error?

Increasing significance level (α). Example: Setting α = 0.10 instead of 0.05.

What increases chance of Type II error?

Decreasing sample size or using a small effect size. Example: Testing a new product with only 5 customers.

Scenario: Reject null, actual true. Type?

Type I error.

Scenario: Fail to reject null, actual false. Type?

Type II error.

True or False: Reducing α reduces Type II error chances.

False. Reducing α increases Type II error chances.

What is the significance level (α) for Type I error?

It is the probability of making a Type I error. Common values: 0.05, 0.01.