Question

HW#9 - Chapter 19 (20pts for turned in on time) 5. (16pts) 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 10 students with similar background. 5 students are randomly chosen to take the workshop, while the other students will serve as a control group. A test is then given to all 10 students and their performances listed below. From the data, can we tell the workshop is effective in improving students' math skills? Control 65 Workshop 70 80 (1) (2pts) There are two groups we need to compare for the study. Control and Workshop. Are those two groups dependent or Independent? Based on your answer, what inference procedure should we apply for this research? (2) (12pts)Please perform the inference you decided in (1), and make sure to follow the 5-step procedure for any hypothesis test. (3) (2pts)Based on your conclusion in (2). what kind of error could you make? Explain the type of error using the context words for this research.

Answer 1

1) Workshop and Control groups are independent. Since 5 different randomly selected people are put into both the groups, and the groups are independent, to perform the test we can use an independent samples t test for the population means.

2) Let 1: Workshop, 2: Control. Now, we are testing,

H0: u1=u2 vs H1: u1>u2

Under H0,

(low N nito,"2 + 2 na 73.2 n = 62.8. 5. = 5.070 S226.611. 1, 250 ₂-5 : Test Statistic: 7312-6218 5.072 6.6112 V 5 5 * = 2.791 #red Now p-value of this one sided 1 Plt 2.791) = 0:0/18 t test h: (fromt tables) since this p-value <x=0.05 l generally accepted level of significance) we have sufficient evidence to Reject fo. 2 3 Soye we can conclude that u zu Die workshop is effective in improving scores We can commit a Typo I erros above Lice. conclude 4,342 When its actually I false. This canke done with probability 0.0118 Cp-value) .