Hypothesis Testing - A decision rule based on data
||Reject Null Hypothesis
||Type I Error
|Do Not Reject Null Hypothesis
||Type II Error
Computing Type II error probabilities
- Example - Let p equal the proportion of defective components in a very large shipment sent to a computer company. The company accepts the shipment only if Ho: p =0.1 can be rejected in favor of Ha: p < 0.1 at a significance level of 0.05 based on a sample of 100 components.
- Compute the probability of failing to reject Ho when the actual percentage of defectives is 7%.
- Compute the probability of failing to reject Ho when the actual percentage is 8%.
- Would the probability of failing to reject Ho increase or decrease if the actual percentage is 9%? Explain your response. (Hint: compare the two probabilities you computed above.)
Power and sample size calculations with R
- Download, install, and explore with the pwr package.
- See Power.R to compute the power on the handout with R
- Explore with the pwr package to compute other powers.
Please complete your reading of Chapter 7 for class on Wednesday.
We will have our second exam on Friday.