Question

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?

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.
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.
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.
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.


answer c

Answer 1

A Type I error occurs when the manager concludes that the adoption rate has dropped below 15% when it actually has not. The consequence is that the manager will not accept more animals into the shelters, thinking there will not be enough room, when there actually is room to care for those animals.

Step-by-step explanation:

A Type I error occurs when the manager concludes that the adoption rate has dropped below 15% when it actually has not. In this context, the consequence of a Type I error is that the manager will not accept more animals into the shelters, thinking there will not be enough room, when there actually is room to care for those animals.