1. Show that the two sample t-test statistic squared (equal variance case) is equal to the single-factor ANOVA F statistic when there are two levels. For simplicity, assume equal sample size of n in each of the two groups. RECALL : Two sided, two independent sample pooled t-test tests the following hypotheses: Hozm=m: H1=mm The test statistic is: Y I - P2 82 P T: % where Y. and 5'; are the sample means in group 1 and 2, respectively. The pooled variance is given by 32+Sz 2_ I 2 sp_ 2 LinkPi 2 where S? and 3% are the sample variances in the group 1 and 2, respectively, S? = QT)