10.5 Power and Probability of Type II Error.notebook
10.5 Power and Probability of Type II Error
March 08, 2017
Power of a test: probability of rejecting the null hypothesis
Effect of Various Factors on the Power of a Test:
1.
The larger the size of the discrepancy between the hypothesized value and the actual value of the population characteristic, the higher the power.
2.
The larger the significance level, α, the higher the power of the test.
3.
The larger the sample size, the higher the power of the test.
Pg 616 Example 10.17
When Ho is false, power = 1 ­ β
Ho: μ = 1.5 versus Ha: μ > 1.5, α = 0.01
P­value = area right of calculated z
reject Ho if calculated z ≥ 2.33
reject if Suppose μ = 1.6 (So Ho is false)
z score for 1.578 = β and Power for t tests:
d = alternative value ­ hypothesized value
σ
= area under z to left of ­0.66 = 0.2546
So if μ = 1.6, β = .2546 25% of all samples would still result in x values less than 1.578 and failure to reject Ho
(Power at μ = 1.6) = 1 ­ (β when μ = 1.6)
= 1 ­ 0.2546
= .7454
What this means? Pg 617
Pg 619 Example 10.19
Appendix Table 5
10.5 Power and Probability of Type II Error.notebook
When the population distribution is normal, the t test for the testing hypothesis about μ has a smaller β than does any other test procedure that has the same level of significance α.
• t test makes β as small as it can be for any significance level
March 08, 2017