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 II error, and what is its consequence in this context

Answer 1

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.

Explanation:

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Answer 2

By accepting a false null hypothesis he committed a type II error.

Explanation:

Type II error is to accept H0 when H0 is false.

If there's a type II error then the null hypothesis is false ie the adoption rate is less than 15 %, when the true adoption rate is not less than 15% . He has accepted the null hypothesis as true and taken the wrong decision of not accepting any new animals into the shelters that week.