A group of 17 students participated in an experiment to test whether a special training session could improve memory. The students were randomly assigned into two groups: A, the experimental group, and B, the control group. The 17 students were initially tested for the ability to recall certain information. Group A was then given special treatment; al B, no. Both groups were examined again, at the end of treatment in group A. The results shown in the following table.

a) Establish the null hypothesis H₀ and the alternate hypothesis H_a that must be used to prove that special training is effective. Suppose that all scores have a normal distribution.

b) Do the data support the hypothesis that special training is effective in improving the ability to remember certain information? Use the significance level α= 0.01

c) State the null hypothesis H₀ and the alternative hypothesis H_a that should be used to prove that in group B the scores of the second evaluation are better than those of the first.

d) Do the data support the hypothesis that in group B the scores of the second evaluation are better than those of the first? Use the significance level α= 0.05

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Group B Students Time of Tes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 23 22 20 21 23 18 17 20 23 22 20 23 17 21 19 20 20 28 29 26 23 31 25 22 26 26 23 25 26 18 21 17 18 20 Group A Students Before After Group B Students Time of Tes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 23 22 20 21 23 18 17 20 23 22 20 23 17 21 19 20 20 28 29 26 23 31 25 22 26 26 23 25 26 18 21 17 18 20 Group A Students Before After