# SOLUTION: 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 w

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 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(57940)   (Show Source): You can put this solution on YOUR website!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 Ho: p = 0.85 H1: p < 0.85 ---------------------------- •Calculate the sample proportion p-hat = 21/50 = 0.42 ---------------------------- •Determine which test statistic applies, and calculate it z(0.42) = (0.42-0.85)/sqrt(0.85*0.15/sqrt(50) = -3.2023 ------------------------------- •Determine the critical value(s). Assuming alpha = 5%, crit value for left tail test = invNorm(0.05) = -1.645 --------------------------------------------- •State your decision: Should the null hypothesis be rejected? Since the test stat is in the reject interval, reject Ho. Reject Ho. ================================== Cheers, Stan H.