Question

A academic tutor wants to assess whether her remedial tutoring has been effective for her five students. She decides to conduct a related samples t-test and records the following grades for students prior to and after receiving her tutoring. Tutoring Before After 2.4 3.1 2.5 2.9 3.0 3.5 2.9 3.1 2.7 3.5 (a) Test whether or not her tutoring is effective at a 0.05 level of significance. State the value of the test statistic. (Round your answer to three decimal places.) t = State the decision to retain or reject the null hypothesis. Retain the null hypothesis Reject the null hypothesis. (b) Compute effect size using estimated Cohen's d. (Round your answer to two decimal places.) d =

Answer 1

Answer)

First we need to find the difference in between after and before

0.7, 0.4, 0.5, 0.2, 0.8

Now we need to find the mean and s.d of the differences

Mean = 0.52

S.d = 0.2387

N = 5

Test statistics t = (mean difference)/(s.d/√n) = 4.871

Degrees of freedom is = n-1 = 4

For 4 dof and 4.871 test statistics

P-value from t distribution is = 0.004

As the obtained p-value is extremely small

We reject the null hypothesis Ho

B)

Effect size = mean difference/s.d = 0.52/0.2387 = 2.18