6.7-6.13

Interpreting P-value (Significance tests)

Assuming (context of Ho), there is a (percent) probability of getting a sample (proportion/mean) of (p/mu) or (more/less) purely by chance.

Conclusion (Significance tests)

Because (p-value) is (less than/greater than) (alpha), we (reject/fail to reject) the Ho. We (have/do not have) convincing evidence of (Ho in context).

Interpreting Power

If the true (proportion/difference in proportions) of (context) is (sample proportion), there is a (Power) probability of correctly rejecting the null of (Ho).

p-value is less than significance level…

significant → reject null

p-value is greater than significance level…

not significant → fail to reject the null

6.8 1) state:

parameter of interest (in context) significance level alpha H0 (always \=) Ha (

6.8 2) plan:

1 sample z-test conditions: 1) rand. sample, 2) 10%, 3) large counts

6.8 3) do:

z-score (standardized test statistic) & p-value w/ graph

6.8 4) conclude:

Because (p-value) is (less than/greater than) (alpha), we (reject/fail to reject) the Ho. We (have/do not have) convincing evidence of (Ho in context).

finding p-value

z-score formula: z\=p-hat-p/(root p(1-p)/n) use chart to find p-value

2-sided test

Ha is not equal to p; multiply p-value by z to get 2-sided p-value

6.11 Hypotheses

H0: p1-p2\=0 (p1\=p2) Ha: p1-p2 , not equal to zero → p1

sample proportion

p-hat \= (x1+x2)/(n1+n2) \= total successes/total sampled

conditions

random for both samples or random assignment; 10% for both samples or state not necessary due to experiment

Type I Error

Truth: H0 true, Conclusion: Reject H0 P(Type I)\=Alpha (Significance Level)

Type II Error

Truth: Ha true, H0 false, Conclusion: Fail to reject H0

Consequences…

Health consequences always considered worse

Power

Truth: Ha true, Conclusion: Reject H0 P(Reject H0 I Ha is true) P(Power)\=1-P(Type II)

Increase Power by:

increasing n, increasing alpha, increasing distance btwn H0 & Ha