AP Stats Important Terms

You reject the null hypothesis when…

• p < α

• There IS sufficient evidence to show…

You fail to reject the null hypothesis when…

• p > α

• There is NOT sufficient evidence to show…

Type II error

• Occurs when you FTR

• Occurs when a null hypothesis that is actually false is not rejected

• False negative

To minimize the risk of a Type II error you can…

• Increase sample size (this increases power of the test)

• Increase significance level

Type I error

• Occurs when you reject

• Occurs when a true null hypothesis is incorrectly rejected

• False positive

• The probability of committing a Type I error is the significance level

To minimize the risk of a Type I error…

• Lower the significance level

• Increase the sample size

Use p̄ when…

• Hypothesis testing - TWO sample populations

• When you’re comparing two proportions

Use p̂ when…

• When estimating population proportion

• Confidence intervals

• Hypothesis testing - ONE sample population

Rules for population mean

• Random sample

• Normal curve OR n ≥ 30

Rules for testing population proportion

• random independent sample

• np and nq > 10

• n < .10N

Rules for testing population mean

• random independent sample

• no outliers

Rules for testing homogeneity

• random independent samples

• all expected values > 5

Rules for testing difference of means

• 2 random independent samples

• n1 ≥ 30

• n2 ≥ 30

• normal

• no outliers

Rules for mean difference

• random DEPENDENT sample (matched pairs)

• normal - n ≥ 30 or no outliers

Use a binomial distribution when…

• fixed independent trials, count successes

• finding the number of successes

• ex: flipping a coin and wanting to find the probability of getting exactly 7 heads

Use a geometric distribution when..

• UNFIXED number of trials

• trials until first success, count trials (UNFIXED)

• when you want to know the probability of success happening on a specific trial

• ex: rolling a die repeatedly until you get a 6, and wondering what the probability that the first 6 happens on the 4th roll