7. An insurance company believes that claim amounts in a certain portfolio of policies follow a normal distribution. An analyst chose 61 policies at random which gave a sample mean of K5,230 and a sample standard deviation of K810. (a) Construct a 95% confidence interval for the mean claim amount in the portfolio. (b) The company has changed its loss assessment processes in order to reduce claim sizes on average, targeting a reduction of K200 compared to the current mean. It does not expect a change to the variability of claim amounts. The company in- tends to verify whether the target has been met by using a sample of claims to idod un
7. An insurance company believes that claim amounts in a certain portfolio of policies follow a normal distribution. An analyst chose 61 policies at random which gave a sample mean of K5,230 and a sample standard deviation of K810. (a) Construct a 95% confidence interval for the mean claim amount in the portfolio. (b) The company has changed its loss assessment processes in order to reduce claim sizes on average, targeting a reduction of K200 compared to the current mean. It does not expect a change to the variability of claim amounts. The company in- tends to verify whether the target has been met by using a sample of claims to idod un
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:7. An insurance company believes that claim amounts in a certain portfolio of policies follow
a normal distribution. An analyst chose 61 policies at random which gave a sample mean
of K5,230 and a sample standard deviation of K810.
(a) Construct a 95% confidence interval for the mean claim amount in the portfolio.
(b) The company has changed its loss assessment processes in order to reduce claim
sizes on average, targeting a reduction of K200 compared to the current mean. It
does not expect a change to the variability of claim amounts. The company in-
tends to verify whether the target has been met by using a sample of claims to
test the null hypothesis that there is no change, against a one-sided alternative hy-
pothesis. Company policy is to perform statistical tests at a significance level of 5%.
Determine the smallest number of claims that would need to be sampled under
the new processes for a K200 reduction to be statistically significant in the test.
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