One measure of student success for colleges and universities is the percent of a

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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.

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 = 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:

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

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

    

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

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

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

State the 2 statistic, degrees of freedom, and the P-value. (Round your answer for 2 to one decimal place and your P-value to four decimal places.)

Conclusion:

We do not have sufficient evidence to conclude that the gateway course had an impact on DFW rate.

We do not have sufficient evidence to conclude that the gateway course had an impact on number of students taking a course.    

We have sufficient evidence to conclude that the gateway course had an impact on DFW rate.

We do not have sufficient evidence to conclude that number of students taking a course had an impact on DFW rate.

We have sufficient evidence to conclude that number of students taking a course had an impact on DFW rate.

Year DFW Rate Number of Students Taking Course Year 1 42.2% 2408 Year 2 24.1% 2325 Year 3 19.7% 2126

Explanation / Answer

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

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

X2 =293.0

df =1

p value=0.0000

We have sufficient evidence to conclude that the gateway course had an impact on DFW rate.

% *students observed Expected Chi square Year Probability O E=total*p =(O-E)^2/E 1 0.333 1016.176 665.11 185.31 2 0.333 560.325 665.11 16.51 3 0.333 418.822 665.11 91.20 1 1995.323 1995.323 293.0127

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