Question 269315:
An insurance company states that 75% of its claims are settled within 5 weeks. A consumer group selected a random sample of 25 of the company’s claims and found 8 of the claims were settled within 5 weeks. Is there enough evidence to support the consumer group’s claim that fewer than 75% of the claims were settled within 5 weeks? Test using the traditional approach with α = 0.05.
· 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 75% of its claims are settled within 5 weeks.
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A consumer group selected a random sample of 25 of the company’s claims and found 8 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 75% of the claims were settled within 5 weeks? Test using the traditional approach with α = 0.05.
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· State the null and alternate hypotheses
Ho: p >= 0.75
H1: p < 0.75
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· Calculate the sample proportion
p-hat = 8/25 = 0.32
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· Determine which test statistic applies, and calculate it
z(0.32) + (0.32 - 0.75)/sqrt[0.75*0.25/75] = -8.6
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· Determine the critical value for left-tail test with alpha = 5%
= invNorm(0.05) = -1.645
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· State your decision: Should the null hypothesis be rejected?
Since the cv is not in the rejection interval, fail to reject Ho.
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Cheers,
Stan H.
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