The following problem:

These quantities might be useful: 2:; 01,5 =12.592, F2213\"; =3.467' mes =2.471. We have the following data summaries: n. =23 , 71 = -0.201 _ 0.940 -0.032 0.129 ' ' _ -0.032 1.001 1. Test H0271. =(0.3, 0.3)' versus H\" :otherwise. Use (1 =0.05. Two new groups of data have been added to the first group. Below are the additional summaries that can be helpful for problems 2 and 3. n2 :17, n3 =10, _ 1.374 _ 0.799 X2 = , a : 0.286 -O.165 _ 0.850 0.052 s _ 1.157 0.184 5 1.425 0.066 2 _ 0.052 0.766 ' 3 _ 0.184 0.498 ' _ 0.066 0.817 Note that S is not the pooled variance. It is the sample variance-covariance matrix calculated ignoring the information about groups. 2. Test H0121 =22 =23 versus Ha :otherwise. Use 0: =0.05. 3, Test H 0 :111 =,u2 2.1.13 versus H\" :otherwise_ Use a :0_05_