Hypothesis Testing - A decision rule based on data
Null Hypothesis
True
False
Decision
Reject Null Hypothesis
Type I Error
Correct Decision
Do Not Reject Null Hypothesis
Correct Decision
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.)