a &B have an Inverse Relationship Reduce probability of one error and the other one goes up. B ∠Y C
a b Reduce probability of one error and the other one goes up. a & b Have an Inverse Relationship
Factors Affecting Type II Error, B True Value of Population Parameter a Increases When Difference between Hypothesized Parameter True Value Decreases Significance level a D Increases When a decreases Population Standard Deviation o D Increases When o Increases βG Sample size n D Increases When n decreases n
• True Value of Population Parameter Increases When Difference Between Hypothesized Parameter & True Value Decreases • Significance Level a Increases When a Decreases • Population Standard Deviation s Increases When s Increases • Sample Size n Increases When n Decreases Factors Affecting Type II Error, b a b b s b n
Z-Test Statistics(o Known) Convert sample statistic(e.g, X)to Standardized z variable X-ux X-u Test Statistic X Compare to Critical Z Value(s) a IfZ test Statistic falls in Critical Region, Reject Ho, Otherwise Do Not Reject Ho
• Convert Sample Statistic (e.g., ) to Standardized Z Variable • Compare to Critical Z Value(s) If Z test Statistic falls in Critical Region, Reject H0 ; Otherwise Do Not Reject H0 Z-Test Statistics (s Known) Test Statistic X n X X Z X X s m s m − = − =
Value test Probability of obtaining a Test Statistic More Extreme (or) than Actual Sample alue Given Ho Is True Called observed level of significance a Smallest Value of a Ho Can Be rejected Used to Make Reiection Decision o If p value ?a, Do Not Reject Ho o Ifp value s a, Reject H(
• Probability of Obtaining a Test Statistic More Extreme ( or ) than Actual Sample Value Given H0 Is True • Called Observed Level of Significance Smallest Value of a H0 Can Be Rejected • Used to Make Rejection Decision If p value ?a, Do Not Reject H0 If p value < a, Reject H0 p Value Test
Hypothesis Testing: Steps Test the Assumption that the true mean of Tv sets in US homes is at least 3 1. State Ho H0:p23 State H H1:<3 2345 Choose a =.05 Choose n n=100 Choose Test. Z Test(orp value
1. State H0 H0 : m ?3 2. State H1 H1 : m < 3 3. Choose a a = .05 4. Choose n n = 100 5. Choose Test: Z Test (or p Value) Hypothesis Testing: Steps Test the Assumption that the true mean # of TV sets in US homes is at least 3