Question

In: Statistics and Probability

An insurance company states that at least 85% of its claims are settled within 30 days.

4) (1 point) An insurance company states that at least 85% of its claims are settled within 30 days. A consumer group selected a random sample of 66 of the company's claims to test this statement. They found that 55 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 85%.

H0H0: The proportion of claims settled within 30 days is equal to 85%

HAHA: The proportion of claims settled within 30 days is less than 85%

2. To setup a simulation for this situation, we let each claim be represented with a card. We take 100 cards, 85 black cards represent claims that are settled within 30 days and 15 red cards represent claims that take longer than 30 days to settle. Shuffle the cards and draw with replacement 66 cards representing the random sample of claims. Calculate the proportion of black cards in the sample and call it  p^simp^sim . Repeat 10,000 times and plot the resulting sample proportions. The p-value will be the proportion of simulations where p^simp^sim is less than or equal to ______________

3) Report your p-value from the app here, rounded to four decimal places:

Solutions

Expert Solution

H0: The proportion of claims settled within 30 days = 85%

HA: The proportion of claims settled within 30 days <  85%

2) To setup a simulation for this situation, we let each claim be represented with a card. We take 100 cards, 85 black cards represent claims that are settled within 30 days and 15 red cards represent claims that take longer than 30 days to settle. Shuffle the cards and draw with replacement 66 cards representing the random sample of claims. Calculate the proportion of black cards in the sample and call it  p^simp^sim . Repeat 10,000 times and plot the resulting sample proportions. The p-value will be the proportion of simulations where p^ sim <= (55 / 66) <=___0.8333___

3)


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