Question

HW#9 - Chapter 18 (20pts for turned in on time) 6. (12pts) To evaluate the effectiveness of a short MATH review workshop for students who need to take the remedial MATH course. A researcher selected a SRS of 5 students, and gave them a math test before the workshop. Another test with the same difficulty level was given after the workshop. And below are the test scores. Provide a statistical test to see if the workshop is effective or not, use 0.05 significance level. Before 65 72 54 60 6 3 After 70 67 80 73 76

Answer 1

6. We use paired to test to check if the workshop was effective or not. Let x be the random samples denoting the scores of the math test before the workshop and y be the random samples denoting the scores of the math test after the workshop. Let 'd' denote the sample difference between x andy and 'D' denote the population difference between X and Y. Then we test the hypothesis, Null hypothesis (Ho): The true mean difference qua) is equal to zero. versus Allernative hypothesis: The bue mean differences (pa) is not equal to zero. The test statistie is, ent(n-1) o o solun where di = xi-yi d = & di/n. Sd = Eldi-d)² n = 5( sample size). -1 1

X I 65 72 L 54 63 67 80 73 76 d=x -Y - 26 - 13 -13 a = -52 = - 10.4 a = -10.4 Sd = {(d; +10,4)² - 130.8. to = -0. 1778 From the table, at 0.05 level of significance, ttab = t10.05/2, -1) = t (0.025, h) = 2.776 (We take 0.025 since it is a two tailed test) Itol = 0.1778 < 2.776 We do not reject Ho. Also, p-value = P(+>ltol) - Plt >0.1778) = 0.1118), which is greater than 0.05. We do not have sufficient evidence to reject Ho and hence the workshop was not effective at 0.05 significance level.