manually conduct the hypothesis test for the two contrasts: please compute the sample contrast, standard error of the contrast, t-statistic of the contrast and p-value.

Contrast 1: H0: -1/2 (1+ 2) +1/2 (3+ 4)=0 Ha: -1/2 (1+ 2) +1/2 (3+ 4)>0

Contrast coefficients : (-1/2, -1/2, 1/2, 1/2, 0),

Contrast 2: H0: 1/2 (3 + 4)-5=0 vs. Ha: 1/2 (3 + 4) -5 0.

Contrast coefficient: (0, 0, 1/2, 1/2, -1)

The sample group means are given below, MSE=1.2005.

Group Mean count

102 3.816667 24

302 4.878788 33

502 4.561538 26

702 4.406667 30

902 3.990476 21

Use R to verify your results.

Friends MeanScore

102 3.817

302 4.879

502 4.562

702 4.407

902 3.990