Question

(12 points) An insurance company states that at least 89% of its claims are settled within 30 days. A consumer group selected a random sample of 61 of the company's claims to test this statement. They found that 51 of the claims were settled within 30 days. Does the consumer group have evidence to disbelieve the insurance company's claim? 1. Write the hypotheses to test if the rate of claims settled within 30 days is less than 89%. Ho: The proportion of claims settled within 30 days is equal to 89%. HA: The proportion of claims settled within 30 days is less than 89%. 2. To setup a simulation for this situation, we let each claim be represented with a card. We take 100 cards, 89 black cards represent claims that are settled within 30 days and 11 red cards represent claims that take longer than 30 days to settle. Shuffle the cards and draw with replacement 61 cards representing the random sample of claims. Calculate the proportion of black cards in the sample and call it Psim - Repeat 10,000 times and plot the resulting sample proportions. The p-value will be the proportion of simulations where peim is less than or equal to 4

Answer 1

The appropriate test for analysis is 'Test for single proportion'. Z =- P-P => N(0,1) P(1-P) Where the sample is proportion and p is the population proportion. n is the sample size. Null hypothesis H: The claim that the insurance company has 89% of claims are settled within 30 days. This implies that, H.:P=0.89 Alternative hypothesis H : The insurance company states that less than 89% of claims are settled within 30 days. This implies, HA:P<0.89 The sample proportion or _51 61 = 0.8361

Test statistic: P-P Z = P1-P N(0,1) 0.8361 -0.89 0.89(1-0.89) V 61 = (-1.35) Compute the value of p from MS excel) p=NORMSDIST(-1.35) =0.088508 0.089 Therefore, the P-value is 0.089. Since p-value is greater than 0.05, so, fail to reject the null hypothesis. Hence, conclude that the claim settled within 30 days is less than 89%.

The appropriate test for analysis is 'Test for single proportion'. P-P — P(1-P) N(0,1) po_2012 Where the sample is proportion and p is the population proportion. n is the sample size. Null hypothesis H.: The claim that the insurance company has 89% of claims are settled within 30 days. This implies that, Ho: P=0.89 Alternative hypothesis H : The insurance company states that less than 89% of claims are settled within 30 days. This implies, H:P<0.89 The sample proportion p = _31 61 = 0.8361

Test statistic: P-P Z = P1-P N(0,1) 0.8361 -0.89 0.89(1-0.89) V 61 = (-1.35) Compute the value of p from MS excel) p=NORMSDIST(-1.35) =0.088508 0.089 Therefore, the P-value is 0.089. Since p-value is greater than 0.05, so, fail to reject the null hypothesis. Hence, conclude that the claim settled within 30 days is less than 89%.