A scientist wants to see if vaccine A is providing more antibody than vaccine B. The scientist drew two random sample with sizes are 45 and 50 from two populations injected with different vaccines. The test results shows that the sam- ple mean antibody level for vaccine A is 1200 while that for vaccine B is 800. The sample variances of the two samples are 300 and 100 respectively. While there is no reliable information about the population variance, it is feasible to assume that the two populations are normally distributed. First consider that population variance for antibody level are the same for both vaccines. (a) What is the null hypothesis? (b) What is the alternative hypothesis? (c) What is the test statistic? (d) What is the p-value for the test statistics? (e) What should be the conclusion for the scientist at 5% level of significance? Now consider the case that population variance for antibody level are the different for different vaccines. 2 (f) What is the test statistic? (g) What is the p-value for the test statistics? (h) What sho