An insurance company offers a discount to homeowners who install smoke detectors in their homes. A company representative claims that 80% or more of policyholders have smoke detectors. You draw a random sample of eight policyholders. Let X be the number of policyholders in the sample who have smoke detectors. a) If exactly 80% of the policyholders have smoke detectors (so the representative's claim is true, but just barely), what is P(X ≤ 1)? b) Based on the answer to part (a), if 80% of the policyholders have smoke detectors, would one policyholder with a smoke detector in a sample of size 8 be an unusually small number? c) If you found that one of the eight sample policy-holders had a smoke detector, would this be convincing evidence that the claim is false? Explain. d) If exactly 80% of the policyholders have smoke detectors, what is P(X ≤ 6)? e) Based on the answer to part (d), if 80% of the policyholders have smoke detectors, would six policy-holders with smoke detectors in a sample of size 8 be an unusually small number? f) If you found that six of the eight sample policy-holders had smoke detectors, would this be convincing evidence that the claim is false? Explain.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
An insurance company offers a discount to homeowners who install smoke detectors in their homes. A company representative claims that 80% or more of policyholders have smoke detectors. You draw a random sample of eight policyholders. Let X be the number of policyholders in the sample who have smoke detectors. a) If exactly 80% of the policyholders have smoke detectors (so the representative's claim is true, but just barely), what is P(X ≤ 1)? b) Based on the answer to part (a), if 80% of the policyholders have smoke detectors, would one policyholder with a smoke detector in a sample of size 8 be an unusually small number? c) If you found that one of the eight sample policy-holders had a smoke detector, would this be convincing evidence that the claim is false? Explain. d) If exactly 80% of the policyholders have smoke detectors, what is P(X ≤ 6)? e) Based on the answer to part (d), if 80% of the policyholders have smoke detectors, would six policy-holders with smoke detectors in a sample of size 8 be an unusually small number? f) If you found that six of the eight sample policy-holders had smoke detectors, would this be convincing evidence that the claim is false? Explain.
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