Asked by Jerry Powell on Jul 02, 2024
Verified
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.
Verified Answer
YM
Youssef Mohamed Reda AbdElHamed AbdElHamed5 days ago
Final Answer :
p = 0.05; p > 0.05; A Type I error would occur if the manufacturer would reject the null hypothesis when, in fact, it is true, i.e., if the manufacturer would conclude the proportion of defective switches is more than 0.05 when, in fact, it is not.; A Type II error would occur if the manufacturer would not reject the null hypothesis when, in fact, it is false, i.e., if the manufacturer would not conclude the proportion defective switches is more than 0.05 when, in fact, it is.; Type II; The Type II error would be the more serious one, since the manufacturer would be keeping a shipment that actually had more than 5% defective switches.; Type I; The Type I error since the supplier would have to take back a shipment even though it does not have more than 5% defective switches.
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.