a) Find the measures of central tendency (mean and median) for the two variables: "Insured.age" and " Credit.score". Discuss the shape of these two distributions. Which measure of central tendency is the best to represent the " Credit.score" data: the mean or the median? (Hint: Use 10% rule.) Discuss your rationale for the choice. b) Find the measures of variability (range, IQR, variance and standard deviation) for the two variables: "Insured.age" and "Credit.score" c) Which one of the two variables, "Insured.age" or " Credit.score", is relatively more variable than the other? (Hint: use the CVs). Question 3 (18 marks) (10+4+4= 18 marks) a) Use the variable "Annual.miles.drive" to construct the confidence intervals for the estimate of the population mean (i.e., mean of annual miles driven), by gender, i.e. by male and female drivers, at 96% levels. Interpret your confidence intervals. b) Did you make any assumptions when constructing your confidence intervals? If yes, which assumptions; if not, why? ) If insurance companies charge premiums based on the annual miles driven, based on your finding, is it warranted for insurance companies to charge male drivers higher premiums based on this data set? Explain. Question 4 (13 marks) (13 marks) Consider the claim that the average credit score of a driver in the given population is 780. Use the data collected for the variable "Credit.score" to test this claim by both critical value approach and p-value approach. (Use the 5% level of significance). Question 5 (23 marks) (15+4+4=23marks) a) Based on your data set, is the average years of no claims ("Years.noclaims") of male drivers is significantly MORE THAN the average years of no claims ("Years.noclaims") of female drivers? Test both critical value and p-value approaches at the 8% level of significance. Note that SPSS only performs a 2-sided test. b) Provide possible reasons why you should expect to find a significant statistical difference between the gender. c) Based on your findings, should the insurance company charge higher premiums based on the gender? Explain your reasoning