Chapter 5.6, Problem 8ES

Questions An insurance company's cumulative incurred claims for the last 5 accident years are given in the following table: Development Year Accident Year 0 2018 1 2 3 4 245 267 274 289 292 2019 255 276 288 294 2020 265 283 292 2021 263 278 2022 271 It can be assumed that claims are fully run off after 4 years. The premiums received for each year are: Accident Year Premium 2018 306 2019 312 2020 318 2021 326 2022 330 You do not need to make any allowance for inflation. 1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method. (b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method. 2. Comment on the differences in the reserves produced by the methods in Part 1.

A population that is uniformly distributed between a=0and b=10 is given in sample sizes ​50(   ​), ​100(   ​), ​250(   ​), and ​500(   ​). Find the sample mean and the sample standard deviations for the given data. Compare your results to the average of means for a sample of size​ 10, and use the empirical rules to analyze the sampling error. For each​ sample, also find the standard error of the mean using formula given below.   Standard Error of the Mean =sigma/Root  Complete the following table with the results from the sampling experiment. ​(Round to four decimal places as​ needed.) Sample Size Average of 8 Sample Means Standard Deviation of 8 Sample Means Standard Error 50       100       250       500

survey of 5050 young professionals found that they spent an average of ​$20.5620.56 when dining​ out, with a standard deviation of ​$11.4111.41. Can you conclude statistically that the population mean is greater than ​$2323​? Use a​ 95% confidence interval.       Question content area bottom Part 1 The​ 95% confidence interval is left bracket nothing comma nothing right bracketenter your response here, enter your response here. As ​$2323 is ▼     of the confidence​ interval, we ▼   can cannot conclude that the population mean is greater than ​$2323. ​(Use ascending order. Round to four decimal places as​ needed.)