Question 250277: An insurance company states that 85% of its claims are settled within 5 weeks. A consumer group selected a random sample of 50 of the company’s claims and found 21 of the claims were settled within 5 weeks. Is there enough evidence to support the consumer group’s claim that fewer than 85% of the claims were settled within 5 weeks? Test using the traditional approach with α = 0.02.
•State the null and alternate hypotheses
•Calculate the sample proportion
•Determine which test statistic applies, and calculate it
•Determine the critical value(s).
•State your decision: Should the null hypothesis be rejected?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! An insurance company states that 85% of its claims are settled within 5 weeks.
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A consumer group selected a random sample of 50 of the company’s claims and found 21 of the claims were settled within 5 weeks.
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Is there enough evidence to support the consumer group’s claim that fewer than 85% of the claims were settled within 5 weeks?
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Test using the traditional approach with α = 0.02.
•State the null and alternate hypotheses
Ho: p = 0.85
H1: p < 0.85
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•Calculate the sample proportion
p-hat = 21/50 = 0.42
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•Determine which test statistic applies, and calculate it
z(0.42) = (0.42-0.85)/sqrt(0.85*0.15/sqrt(50) = -3.2023
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•Determine the critical value(s).
Assuming alpha = 5%, crit value for left tail test = invNorm(0.05) = -1.645
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•State your decision: Should the null hypothesis be rejected?
Since the test stat is in the reject interval, reject Ho.
Reject Ho.
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Cheers,
Stan H.
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