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February 7th, 2017, 10:28 AM  #1 
Newbie Joined: Feb 2017 From: Macedonia, Struga Posts: 3 Thanks: 0  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. 
February 7th, 2017, 10:33 AM  #2  
Senior Member Joined: Sep 2015 From: USA Posts: 1,847 Thanks: 953  Quote:
 
February 7th, 2017, 10:40 AM  #3 
Newbie Joined: Feb 2017 From: Macedonia, Struga Posts: 3 Thanks: 0 
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$. 
February 7th, 2017, 11:13 AM  #4 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 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) 
February 8th, 2017, 06:16 AM  #5 
Newbie Joined: Feb 2017 From: Macedonia, Struga Posts: 3 Thanks: 0 
a) n=40 x=1650 alpha= 0,05 beta= 350 z=(16501500)/(350/ root of 40)= 2,71 b) idk how to solve this one 

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