Chapter Nine

type I error

occurs if a test rejects the null when the null is true. that is, the test finds convincing evidence that the alternative hypothesis is true when it really isn’t

type II error

occurs if a test fails to reject the null when the null is true. that is, the test does not find convincing evidence that the alternative hypothesis is true when it is

as sample size increases

test power: increases

type I: stays the same

type II: decreases

probability of a type I error

the significance level is the probability of a type I error

probability of a type II error

a type II error is inversely related to the probability of a type I error

conclusion

because our p-value is 0.637 > a = 0.05, we fail to reject the null. there is not convincing evidence that the true proportion of \[context\] differs from 25%

when the p-value is less than the significance value

we reject the null

when the p-value is more than the significance value

we fail to reject the null

as significance level increases

test power: increases

type I: increases

type II: decreases

as the null and true value get farther apart

test power: increases

type I: stays the same

type II: decreases