An insurance company offers a discount to homeowners who install smoke detectors in their homes. A company

Question:

An insurance company offers a discount to homeowners who install smoke detectors in their homes. A company representative claims that 80% or more of policy holders have smoke detectors. You draw a random sample of 8 policy holders.

a. If exactly 80% of the policy holders have smoke detectors

(so the representative’s claim is true, but just barely), what is the probability that at most 2 of the 8 sampled policy holders have smoke detectors?

b. Based on the answer to part (a), if 80% of the policy holders have smoke detectors, would 2 policy holders with smoke detectors in a sample of size 8 be an unusually small number?

c. If you found that 2 of the 8 sample policy holders had a smoke detector, would this be convincing evidence that the claim is false? Explain.

d. If exactly 80% of the policy holders have smoke detectors, what is the probability that at most 6 of the 8 sampled policy holders have smoke detectors?

e. Based on the answer to part (d), if 80% of the policy holders have smoke detectors, would 6 policy holders with smoke detectors in a sample of size 8 be an unusually small number?

f. If you found that 6 of the 8 sample policy holders had smoke detectors, would this be convincing evidence that the claim is false? Explain.

Step by Step Answer:

Related Book For  book-img-for-question

Elementary Statistics

ISBN: 9781259969454

3rd Edition

Authors: William Navidi, Barry Monk

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