Question 8 of 25 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
Animal shelters in a county need at least 15% of their animals to be adopted weekly to have room for the new animals that are brought into the various shelters. The county manager takes a random sample of shelters each week to estimate the overall proportion of animals that are adopted. If he concludes that the proportion has dropped below 15%, he will not accept any new animals into the shelters that week. He tests the hypotheses: H0: The adoption rate is 15%, and Ha: The adoption rate is less than 15%. What is a Type I error, and what is its consequence in this context?
Answer
A
The manager believes the adoption rate is still 15%, when it actually has dropped below 15%. The manager will accept more animals into the shelters and will run out of room.
B
The manager believes the adoption rate has dropped below 15%, when it actually has not. The manager will accept more animals into the shelters and will run out of room.
C
The manager believes the adoption rate has dropped below 15%, when it actually has not. The manager will not accept more animals into the shelters, when there actually is room to care for those animals.
D
The manager believes the adoption rate is still 15%, when it actually has dropped below 15%. The manager will not accept some animals into the shelters, thinking there will not be enough room, when they could have taken care of those animals.