Factor Vis a protein involved in the forming of blood clots. The higher the level of factor V, the faster the blood clots. The Auckland Blood Transfusion Service sterilizes its blood donations, but is concerned that factor V levels may be decreased by sterilization. To assess the possibility, the clinic measures blood levels of factor V for 16 blood samples before and after sterilization. The data appear below. Factor V levels Subject Pre-sterilization Post-sterilization 1073 916 1064 1030 967 923 849 892 810 628 855 759 1047 828 1008 784 957 809 829 773 821 786 1257 1106 1095 832 1098 863 15 932 783 16 1440 869 a) Estimate the change in the mean level of factor V with a two-sided 95% confidence interval b) Using a 5% level of significance, conduct a statistical test whether sterilization significantly reduces mean factor V levels or not. State null and alternate hypotheses, estimate critical value, test statistics and your conclusions