Question

A reading test was administered to both a control group and an experimental
group after 6 weeks of instruction during which the experimental group received
peer tutoring and the control group did not. The average score for the 30 subjects
in the control group of the vocabulary portion of the test was 349.2 with standard
deviation of 56.6. For the experimental group of 30 children, the mean score on
the same portion of the test was 368.4 with standard deviation 39.5. Use a 1%
level of significance to test the claim that the experimental group performed better
than the control group.

Answer 1

Here experimental group means the or not. VS Vs nz Let u, denote the mean score of the experimental өчP in the nocabulary portion of the test. M, denote the same for the control group. ЯР who received peer tutoring for a meets and control group didn't receive any tutoring for the same span of time. We want to test whether the experimental group performed better than the control group ie to test the following hypotheses. Ho: M, =lz H, M, > uz equivalently Ho : M - M₂ 20 H.M.-> o Now let ne and denote the sample size for control experimental and group group respectively. X, and a denote the for experimental group & control group respectively. Also let s, and a denote the sample standard deviations for experimental group & control group respectively. Then the test statistic for testing H, is given by, T= (Fi-72) S? Az Nowe under Ho Tnt, Hence the critical ntn₂-2 value / cut off value for this test statistic at level L is given by ta; n, the mean scores Hous + Here nan₂ = 30 tool to. 22.392377 0.01, 58 Here 2 = 17:=0.01 0.01; 30+30-2 reject to if (obtained from t-table). Hence we T> 2.392377

None X = 368.4 we are ginen n,=h₂=30 7 = 349.2 s, = 39.5 sz 56.6 368.4- 349.2 19.2 . Ta = 1.52365 12.6013359 (39.5) . (56-6) 30 30 Hence Ho at TL 2.392377 and hence we fail to reject It duel significance and conclude on the basis of ginen data that, there is not enough evidence to support the claim that experimental group performed better than the control group the test. in