3. Measles is a highly contagious infectious disease which was declared eradicated from the US in 2000 due to the success of vaccination efforts. Consider the following data on vaccination rates for measles collected from students entering kindergarten in Washington. Year Sample Size|Sample Vaccination Rate 2000 8750 95.44% 2009 7875 93.60% (a) Has the vaccination rate of students stayed the same or decreased since 2000? Conduct a hypothesis test at a significance level of 1% for Ho : P2000 = P2009 VS. H1 : P2000 > P2009, where p2ooo and p2009 are the population vaccination rates for years 2000 and 2009, respectively. Propose the most appropriate test statistic and report your decision. (b) To achieve herd immunity for measles, at least 93% of the population needs to be vacci- nated. Was herd immunity achieved in the population of students entering kindergarten in 2009? Conduct a hypothesis test at a significance level of 1%. Formulate the null and alternative hypotheses, propose a test statistic, and report your decisions. (c) How large should the sample size be so that with 99% confidence the population vacci- nation rate of 2009 is at least 93%? (Assume that adding additional samples does not change the sample vaccination rate.)