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...

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Extracted 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.