During the fall semester of 2014, the University of North Georgia developed a corequisite College Algebra course. In this approach, students who would otherwise place in a Learning Support (LS) course in one semester and then enroll in College Algebra the subsequent semester (upon successful completion of the LS course) would instead enroll in corequisite College Algebra. In this course, students were taught prerequisite material for the College Algebra course on a just-in-time basis in an LS course while also enrolled in College Algebra. To determine if this method of instruction was effective, 163 students participated in a study from fall 2014 through spring 2015. There were 77 students in corequisite College Algebra and 86 students in traditional College Algebra.

(a) To measure knowledge gained in each course (that is, student improvement), Hake’s gain ratio was utilized. 

Gain = (Final Exam Score - Pretest Score)/(100 - Pretest Score) # 100 

The table in the next column shows the mean and standard deviation gain score for both the corequisite College Algebra and traditional College Algebra. Does the evidence suggest a difference in gain between the two courses at the α = 0.05 level of significance? If so, estimate the difference in gain between the two courses with 95% confidence.

(b) In addition to improvement between the two courses, the researchers considered grade distribution. The table below is the grade distribution between the corequisite College Algebra and traditional College Algebra. Is grade earned in the course independent of course type? If there is an association between grade and course type, describe the association. Use a 0.05 level of significance.

(c) Assuming that passing for this class is a grade of D or higher, what proportion of the students passed the corequisite College Algebra? What proportion of the students passed the traditional College Algebra?
(d) Is there evidence to suggest the pass rates in corequisite College Algebra are different from those in traditional College Algebra at the α = 0.05 level of significance? If so, estimate the difference with 95% confidence.

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n Mean Standard Deviation Corequisite 77 56.3 20.3 Traditional 86 45.9 38.3