Type I and II Errors

1. Type I and II Errors What are type I and II errors and what do they mean?

2. The truth about the Null You never really know the truth about the Null Hypothesis, all you really know is what your sample tells you. We never really are sure if we make mistakes or not when we reject or fail to reject the Ho So, we measure the probability that we might make a mistake. We give the two possible mistakes names: Type I and Type II

3. There are 4 possible outcomes with a hypothesis test. Pg 1.2 You Fail to Reject the Null Hypothesis & it is true – you’re right! You Fail to Reject the Null Hypothesis & it is false – you’re wrong Type I Error You Reject the Null Hypothesis & it is false – you’re right! You Reject the Null Hypothesis & it is true – you’re wrong! Type II Error

4. Put in table format it looks like this.

5. Beads! You have been given a sample of beads. Pick a color to test – every one at your table must pick a different color – and count how many of the beads are your color. The company says they make 25% of each color bead. Set up a Hypothesis test to test their claim. Pg1.4 choose color Pg 1.5 count – find phat

6. Beads! Hypothesis in picture format The company says they make 25% of each color bead. Set up a Hypothesis test to test their claim with your color bead.. Population for Ho P-value 0.25 C.I. - % certain that Population % falls in this interval Sample 0.267

7. Beads! You have been given a sample of beads. Pick a color to test – every one at your table must pick a different color – and count how many of the beads are your color. The company says they make 25% of each color bead. Set up a Hypothesis test to test their claim. Find Assumptions: Hypothesis Statement Find Assumptions: Hypothesis Statement Null Hypothesis: Alternate Hypothesis Find Assumptions: Hypothesis Statement Null Hypothesis: Alternate Hypothesis Critical value: Alpha Level: Find Assumptions: Hypothesis Statement Null Hypothesis: Alternate Hypothesis Critical value: Alpha Level: Z-score: P-value for test: Find Assumptions: Hypothesis Statement Null Hypothesis: Alternate Hypothesis Critical value: Alpha Level: Z-score: P-value for test: Conclusion: Pg1.6 assumptions Pg 1.7 Ho & Ha Pg 1.8 alpha Pg 1.9 z & p-value Pg 1.10 error type

8. Beads! Which type of error might you have made? Explain it in context.

9. The definitions as pictures Null distribution Sample distribution applet

10. A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that employee inattention is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to offer incentives to employees who have lower defect rates on their shifts. The incentive program is instituted for 1 month. If successful, the company will continue with the incentive program.

11. A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that employee inattention is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to offer incentives to employees who have lower defect rates on their shifts. The incentive program is instituted for 1 month. If successful, the company will continue with the incentive program.

12. A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that employee inattention is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to offer incentives to employees who have lower defect rates on their shifts. The incentive program is instituted for 1 month. If successful, the company will continue with the incentive program.

13. A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that employee inattention is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to offer incentives to employees who have lower defect rates on their shifts. The incentive program is instituted for 1 month. If successful, the company will continue with the incentive program.

14. A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that employee inattention is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to offer incentives to employees who have lower defect rates on their shifts. The incentive program is instituted for 1 month. If successful, the company will continue with the incentive program.

15. A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that employee inattention is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to offer incentives to employees who have lower defect rates on their shifts. The incentive program is instituted for 1 month. If successful, the company will continue with the incentive program.

16. A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that employee inattention is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to offer incentives to employees who have lower defect rates on their shifts. The incentive program is instituted for 1 month. If successful, the company will continue with the incentive program.

17. A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that employee inattention is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to offer incentives to employees who have lower defect rates on their shifts. The incentive program is instituted for 1 month. If successful, the company will continue with the incentive program.