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February 7th, 2017, 10:28 AM   #1
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Question Probability problem with Insurance company Help

An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average clam amount was $1500. They are concerned that the true mean is actually higher than this, because they could potentially lose a lot of money. They randomly select 40 claims, and calculate a sample mean of $1650. Assuming that the standard deviation of claims is $350, test to see if the insurance company should be concerned.
a) Does the test confirms the concern of the insurance company that the true mean is actually higher than $1500, with acceptable risk of 1$?
b) Calculate the total error if the probability that the average claim amount is higher than $1500 is 5$, and the power of the test is 95$.

Last edited by zupanii; February 7th, 2017 at 10:38 AM.
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February 7th, 2017, 10:33 AM   #2
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Originally Posted by zupanii View Post
An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average clam amount was \$1500. They are concerned that the true mean is actually higher than this, because they could potentially lose a lot of money. They randomly select 40 claims, and calculate a sample mean of \$1650. Assuming that the standard deviation of claims is \$350, test to see if the insurance company should be concerned.
a) Does the test confirms the concern of the insurance company that the true mean is actually higher than \$1500, with acceptable risk of 1\$?
b) Calculate the total error if the probability that the average claim amount is higher than \$1500 is 5\$, and the power of the test is 95$.
dollars escaped for readability
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February 7th, 2017, 10:40 AM   #3
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An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average clam amount was $1500. They are concerned that the true mean is actually higher than this, because they could potentially lose a lot of money. They randomly select 40 claims, and calculate a sample mean of $1650. Assuming that the standard deviation of claims is $350, test to see if the insurance company should be concerned.
a) Does the test confirms the concern of the insurance company that the true mean is actually higher than $1500, with acceptable risk of 1$?
b) Calculate the total error if the probability that the average claim amount is higher than $1500 is 5$, and the power of the test is 95$.
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February 7th, 2017, 11:13 AM   #4
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Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics
Can you show us you understand the question first?

-What are the null and alternative hypotheses?
-Which test should you use? (Hint: the population SD is given)
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February 8th, 2017, 06:16 AM   #5
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a)
n=40
x=1650
alpha= 0,05
beta= 350

z=(1650-1500)/(350/ root of 40)= 2,71

b) idk how to solve this one
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