Question

(12 points) An insurance company states that at least 88% of its claims are settled within 30 days. A consumer group selected a random sample of 67 of the company's claims to test this statement. They found that 57 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 88%. Ho: The proportion of claims settled within 30 days is equal to 88%. HA: The proportion of claims settled within 30 days is less than 88%. 2. To setup a simulation for this situation, we let each claim be represented with a card. We take 100 cards, 88 black cards represent claims that are settled within 30 days and 12 red cards represent claims that take longer than 30 days to settle. Shuffle the cards and draw with replacement 67 cards representing the random sample of claims. Calculate the proportion of black cards in the sample and call it sim. Repeat 10,000 times and plot the resulting sample proportions. The p-value will be the proportion of simulations where psim is less than or equal to 1 3. Use the One Proportion Resampling test app embedded here to perform the simulation. Draw at least 3000 samples. Report your p-value from the app here, rounded to four decimal places:

I need help with the last question in #2 and I need help with #3

Answer 1

2) .....................where psim is less than 57/67=0.8507

3)

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null Hypothesis: Ho: alternate Hypothesis: Ha: 0.880 0.880 1.645 for 0.05 level with left tailed test, critical value of z= Decision rule: reject Ho if test statistic z < -1.645 sample success sample size 67.0 std error =Se = (p*(1-p)/n) = 0.0397 sample proportion p x/n= 0.8507 test stat = Z (f-p)/Se= -0.74 p value 0.2302

p value =0.2302