just this please

Problem 6 (22pt) Suppose we have the following two sample data where the two samples have the same size(Table 2). Index 1 12 sample 1 3,00 19 ... 146 sample 2 1.60 -2.36 181 2.32 Table 2: Two sample data Let's write sample 1 as x = (21, 12. ... .ria) and sample ? as y = (21.92,-.. . Mis) (ez. 21 = 3.00) and y1 - 1.60). x and y satisfy * = 1.0,1 = 0.45, 8; = 1.30, 8 = 2.49 Now we want to test if the two population means are equal, Le, we test Hop - pays Hi : my pz. (a) Suppose the two samples are from independent normal distributions with equal variances(unknown] In other words, our model is Xi, X1, Xin " N(, s'), (i) (3pt) Write the test statistic and its distribution under Ho. (ii) (4pt) Compute the value of the realized test statistic, 7 (iii) (4pt) Compute the p value. What do you conclude at level o = 0.057 (b) Now assume that this is a paired data. Let dy - 2, - y be the difference of the ith observations and assume that the differences follow a normal distribution, i.c., where up - in - us and ap is an unknown positive constant. The sample variance of dy's is given by = = 0.20. (i) (3pt) Write the test statistic and its distribution under Ho. (ii) (4pt) Compute the value of the realized test statistic. (iii) (4pt) Compute the p value. What do you conclude at level a = 0.057