Question 4 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
A plant in Alamo, TN, manufactures complex transformer components that must meet specific guidelines for safety. One such component is constructed to deliver 1,000 volts of electricity. A component creates a critical safety hazard if it absorbs humidity at a level above 3%. Any components that absorb too much humidity will be destroyed. A quality control inspector uses a random sample of components to conduct a hypothesis test with H0: The humidity level absorbed is 3%, and Ha: The humidity level absorbed is more than 3%. What is a Type I error in this context?
Answer
A
A Type I error would result in failing to reject a false null hypothesis. This means the company would believe the humidity level is at most 3%, when in fact it exceeds 3%.
B
A Type I error would result in rejecting a true null hypothesis. This means the company would believe the humidity level is more than 3%, when in fact it is not more than 3%.
C
A Type I error would result in rejecting a true null hypothesis. This means the company would believe the voltage delivered is more than 1,000 volts, when the voltage is actually not more than 1,000 volts.
D
A Type I error would result in failing to reject a false null hypothesis. This means the company would believe the voltage delivered is no more than 1,000 volts, when the voltage is actually more than 1,000 volts.