Question

One measure of student success for colleges and universities is the percent of admitted students who graduate. Studies indicate that a key issue in retaining students is their performance in so-called gateway courses. These are courses that serve as prerequisites for other key courses that are essential for student success. One measure of student performance in these courses is the DFW rate, the percent of students who receive grades of D, F, or W (withdraw). A major project was undertaken to improve the DFW rate in a gateway course at a large midwestern university. The course curriculum was revised to make it more relevant to the majors of the students taking the course, a small group of excellent teachers taught the course, technology (including clickers and online homework) was introduced, and student support outside the classroom was increased. The following table gives data on the DFW rates for the course over three years. In Year 1, the traditional course was given; in Year 2, a few changes were introduced; and in Year 3, the course was substantially revised.

Year	DFW Rate	Number of Students Taking Course
Year 1	42.1%	2408
Year 2	24.3%	2325
Year 3	19.4%	2126

Do you think that the changes in this gateway course had an impact on the DFW rate? Support your answer by an analysis of the data. (Use α = 0.01.)

State the null and alternative hypotheses.
Null Hypothesis:

H₀: The gateway course did not have an impact on DFW rate.

H₀: Gateway course did not have an impact on number of students taking a course.

    

H₀: The gateway course had an impact on DFW rate.

H₀: Number of students taking a course did not have an impact on DFW rate.

H₀: Number of students taking a course had an impact on DFW rate.

Alternative Hypothesis:

H_a: The gateway course did not have an impact on DFW rate.

H_a: The gateway course did not have an impact on number of students taking a course.

    

H_a: The gateway course had an impact on DFW rate.

H_a: Number of students taking a course did not have an impact on DFW rate.

H_a: Number of students taking a course had an impact on DFW rate.

State the χ² statistic, degrees of freedom, and the P-value. (Round your answer for χ² to one decimal place and your P-value to four decimal places.)

χ2	=
df	=
P-value	=

Answer 1

The statistical software output for this problem is:

Hence,

Ho: The gateway course did not have an impact on DFW rate.

Ha: The gateway course had an impact on DFW rate.

= 320.6

DF = 2

P - value = 0.0000