Asked by Jerry Powell on Jul 02, 2024
A toaster manufacturer receives large shipments of thermal switches from a supplier. A sample from each shipment is selected and tested. The manufacturer is willing to send the shipment back if the proportion of defective switches is more than 5%. Otherwise, the shipment will be kept.
State the appropriate null and alternative hypotheses to be tested by the manufacturer.
H0: ______________
H1: ______________
Describe the Type I error.
________________________________________________________
Describe the Type II error for this problem.
________________________________________________________
From the manufacturer's point of view, which error would be the more serious?
______________
Justify your answer.
________________________________________________________
From the supplier's point of view, which error would be the more serious?
______________
Justify your answer.
________________________________________________________
Type I Error
A statistical mistake made when a true null hypothesis is incorrectly rejected.
Type II Error
A statistical mistake that occurs when a false null hypothesis is not rejected, erroneously indicating no effect or difference when one does exist.
- Gain an understanding of and generate null and alternative hypotheses for distinct real-world contexts.
- Distinguish between Type I and Type II errors in hypothesis testing and explain their outcomes.
- Comprehend and elucidate the practical ramifications of Type I and Type II errors for diverse stakeholders.
Learning Objectives
- Gain an understanding of and generate null and alternative hypotheses for distinct real-world contexts.
- Distinguish between Type I and Type II errors in hypothesis testing and explain their outcomes.
- Comprehend and elucidate the practical ramifications of Type I and Type II errors for diverse stakeholders.