Type I and II Errors

What are type I and II errors and what do they mean?

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

The truth about the Null

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

You Reject the Null Hypothesis & it is true – you’re wrong!

You Reject the Null Hypothesis & it is false – you’re right!

Type I Error

Type II Error

Put in table format it looks like this.

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.

Pg 1.4 choose colorPg 1.5 count – find phat

Beads! Hypothesis in picture formatThe company says they make 25% of each color bead. Set up a Hypothesis test to test their claim with your color bead..

0.25

0.267

Population for Ho

Sample

P-value

C.I. - % certain that Population % falls in this interval

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.

FindAssumptions: Hypothesis StatementFindAssumptions: Hypothesis StatementNull Hypothesis: Alternate Hypothesis

FindAssumptions: Hypothesis StatementNull Hypothesis: Alternate HypothesisCritical value: Alpha Level:

FindAssumptions: Hypothesis StatementNull Hypothesis: Alternate HypothesisCritical value: Alpha Level:Z-score: P-value for test:

FindAssumptions: Hypothesis StatementNull Hypothesis: Alternate HypothesisCritical value: Alpha Level:Z-score: P-value for test:Conclusion: Pg 1.6 assumptions

Pg 1.7 Ho & HaPg 1.8 alphaPg 1.9 z & p-valuePg 1.10 error type

Beads!Which type of error might you have made?

Explain it in context.

The definitions as pictures

Sample distribution

Nulldistribution

applet

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.

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.

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.

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.

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.

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.

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.

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.