1. The Probability of a Type II Error and the Power of the Test

2. Probability of a Type II Error / Power of Test
Type I Error: Rejecting Null Hypothesis when Null Hypothesis is true (α is the probability of a Type I Error)
Type II Error: Accepting Null Hypothesis when Null Hypothesis is false.

3. Review: How to Determine Picture
H1: p ≠ value Two Tails H1: p < value Left Tail H1: p > value Right Tail

4. Finding Probability of a Type II Error / Power of Test (Proportion) (TI-83/84)
Write down claim
Write down null and alternate hypothesis
Draw picture (determine tail(s))
Find ZAL and/or ZAR (you will have both for two tails) – round to 3 decimal places Left Tail: ZAL = INVNORM(α) Right Tail: ZAR = INVNORM(1-α ) Two Tails: ZAL = INVNORM(α/2) and ZAR = INVNORM(1-α/2)

5. Finding Probability of a Type II Error / Power of Test (Proportion) (TI-83/84)

6. Finding Probability of a Type II Error / Power of Test (Proportion) (TI-83/84)

7. Finding Probability of a Type II Error / Power of Test (Proportion) (TI-83/84)
7. Find the Probability of a Type II Error (β)
Left Tail: β = NORMALCDF(zL,E99)
Right Tail: β = NORMALCDF(-E99,zR)
Two Tails: β = NORMALCDF(zL,zR)
8. Find the power of the test (1-β)

8. Finding Probability of a Type II Error / Power of Test (Proportion) (By Hand)
Write down claim
Write down null and alternate hypothesis
Draw picture (determine tail(s))
Find ZAL and/or ZAR (you will have both for two tails) – Use Standard Normal Distribution table Left Tail: ZAL = Look up α Right Tail: ZAR = Look up (1-α) Two Tails: ZAL = Look up (α/2) and ZAR = Look up (1-α/2)

9. Finding Probability of a Type II Error / Power of Test (Proportion) (By Hand)

10. Finding Probability of a Type II Error / Power of Test (Proportion) (By Hand)

11. Finding Probability of a Type II Error / Power of Test (Proportion) (By Hand)
7. Find the Probability of a Type II Error (β). Look up z scores in standard normal distribution table.
Left Tail: β = 1 – (value from table based on zL)
Right Tail: β = (value from table based on zR)
Two Tails: β = (value from table based on zR) – (value from table based on zL)
8. Find the power of the test (1-β)

12. 1. Find Probability of Type II Error / Power of Test
To test Ho: p = 0.40 versus H1: p < 0.40, a simple random sample of n = 200 is obtained and 90 successes are observed. If the researcher decides to test this hypothesis at the α = 0.05 level of significance, compute the probability of making a Type II Error if the true population proportion is What is the power of the test?

13. 2. Find Probability of Type II Error / Power of Test
To test Ho: p = 0.30 versus H1: p ≠ 0.30, a simple random sample of n = 500 is obtained and 170 successes are observed. If the researcher decides to test this hypothesis at the α = 0.01 level of significance, compute the probability of making a Type II Error if the true population proportion is What is the power of the test?

14. Finding Probability of a Type II Error / Power of Test (Mean) (TI-83/84)
Write down claim
Write down null and alternate hypothesis
Draw picture (determine tail(s))
Find ZAL and/or ZAR (you will have both for two tails) – round to 3 decimal places Left Tail: ZAL = INVNORM(α) Right Tail: ZAR = INVNORM(1-α) Two Tails: ZAL = INVNORM(α/2) and ZAR = INVNORM(1-α/2)

15. Finding Probability of a Type II Error / Power of Test (Mean) (TI-83/84)

16. Finding Probability of a Type II Error / Power of Test (Mean) (TI-83/84)

17. Finding Probability of a Type II Error / Power of Test (Mean) (TI-83/84)
7. Find the Probability of a Type II Error (β)
Left Tail: β = NORMALCDF(zL,E99)
Right Tail: β = NORMALCDF(-E99,zR)
Two Tails: β = NORMALCDF(zL,zR)
8. Find the power of the test (1-β)

18. Finding Probability of a Type II Error / Power of Test (Mean) (By Hand)
Write down claim
Write down null and alternate hypothesis
Draw picture (determine tail(s))
Find ZAL and/or ZAR (you will have both for two tails) – Use Standard Normal Distribution table Left Tail: ZAL = Look up α Right Tail: ZAR = Look up (1-α) Two Tails: ZAL = Look up (α/2) and ZAR = Look up (1-α/2)

19. Finding Probability of a Type II Error / Power of Test (Mean) (By Hand)

20. Finding Probability of a Type II Error / Power of Test (Mean) (By Hand)

21. Finding Probability of a Type II Error / Power of Test (Mean) (By Hand)
7. Find the Probability of a Type II Error (β). Look up z scores in standard normal distribution table.
Left Tail: β = 1 – (value from table based on zL)
Right Tail: β = (value from table based on zR)
Two Tails: β = (value from table based on zR) – (value from table based on zL)
8. Find the power of the test (1-β)

22. 3. Find Probability of Type II Error / Power of Test
To test Ho: μ = 400 versus H1: μ > 400, a simple random sample of n = 100 is obtained. Assume the population standard deviation is 80. If the researcher decides to test this hypothesis at the α = 0.05 level of significance, compute the probability of making a Type II Error if the true population mean is What is the power of the test?