Explain, the following questions adequately.
Q4. (a) Survival times are available for four insureds, two from risk class A and two from risk class B. The two from risk class A passed away at times t = 1 and t = 9. The two from risk class B died at times t = 2 and t = 4. Using the Empirical Credibility Model I, estimate the credibility factor Z. [Marks 8] (b) An investigative journalist comes across information about two policy groups administered by an insurance company. The data however has missing values for some years in total losses and numbers in policy groups as shown in the following table. The missing values are represented by the symbol * Policy group Year 1 Year 2 Year 3 Year 4 Total Losses 750 600 Number in group 3 2 Total Losses 975 1200 900 Number in group 5 6 4 5 Using the Empirical Credibility Model II, determine the premium for each policyholder in Year 4. [Marks 8]1. Given that 210 out of a sample of 615 recent college graduates indicated they had graduated from college in four years, what will the sample proportion (or p) be? Please compute this value below and round your answer to three decimal places. a. To be able to conduct a hypothesis test, we will now need to compute a test statistic (using the following formula). Please attempt to compute this test statistic below, showing as much work as you can. I p - p Z = p (1 - p) n b. Remember that as part of the process of conducting a hypothesis test, we need to find what's called a probability value, or a p-value for short. This p-value value tells us something about how likely it would be to observe results at least as extreme as what we observed, if the null hypothesis is really true. Based on the test statistic you calculated to answer Question 6, what should the p-value be equal to? Please use Table B to find this p-value. (Hint: Don't forget that since a p-value is a probability, you need to now take the percentile you get from Table B and divide it by 100 to convert it to a probability). We determine if we should reject the null hypothesis based on how the p-value compares to our chosen significance level. If we assume here that we are using a significance level (or an alpha level) of 0.05, should we reject the null hypothesis or fail to reject the null hypothesis? Please explain the reason for your answer. d. If a larger significance level had been chosen-like 0.10-would you have made a different decision (compared to the decision you explained in your answer to Question 8) about whether to reject or fail to reject the null hypothesis? Please explain. C. If a smaller significance level had been chosen-like 0.01-would you have made a different decision (compared to the decision you explained in your answer to Question 8) about whether to reject or fail to reject the null hypothesis? Please explain.Statistical Inference: One Population Binomial Distribution Hypothesis Testing 1. Consider drawing a random sample of size n = 100 of a random variable X that has a Bernoulli distribution with probability of success p = .75. (a) What is P(p 2 .98)? Note that this can be answered with an approximation or with an exact value. If you are using an approximation, explain why the approximation is valid. (b) What is P(p
