One measure of student success for colleges and universities is the percent of a
ID: 3312552 • Letter: O
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.
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 42.8% 2408 Year 2 24.3% 2325 Year 3 19.5% 2126Explanation / Answer
H0: The gateway course did not have an impact on DFW rate.
Ha: The gateway course had an impact on DFW rate.
The P-Value is < 0.00001. The result is significant at p < 0.05.
We have sufficient evidence to conclude that the gateway course had an impact on DFW rate.
Observed Year 1 Year 2 Year 3 Total DFW 1031 565 415 2011 No DFW 1377 1760 1711 4848 Total 2408 2325 2126 6859 Expected Year 1 Year 2 Year 3 Total DFW 706.004957 681.6700685 623.3249745 2010 No DFW 1701.995043 1643.329931 1502.675026 4849 Total 2408 2325 2126 6859 (O-E)^2/E Year 1 Year 2 Year 3 Total DFW 149.6048674 19.96846498 69.6254711 239.1988035 No DFW 62.05762961 8.28312357 28.88135775 99.22211093 Total 211.662497 28.25158855 98.50682885 338.4209144 chi-square DF (r-1)(c-1) 2The P-Value is < 0.00001. The result is significant at p < 0.05.
We have sufficient evidence to conclude that the gateway course had an impact on DFW rate.
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