Problem 1

Calculus 1 is a difficult course for students across the country. It has one of the highest DFW (students with grades of D or F, or withdrew) rates of all college courses. A small mid-western university wanted to examine if the primary type of instruction (lecture, facilitation, hybrid) among professors was associated with student grades (A-F). Below is SPSS output from a statistical analysis:

method * grade Crosstabulation grade A B C D FW Total method facilitation Count 12 14 11 7 2 46 Expected Count 9.0 10.4 13.8 8.7 4.0 46.0 % within method 26.1% 30.4% 23.9% 15.2% 4.3% 100.0% hybrid Count 24 27 26 17 5 99 Expected Count 19.5 22.4 29.7 18.8 8.6 99.0 % within method 24.2% 27.3% 26.3% 17.2% 5.1% 100.0% lecture Count 23 27 53 33 19 155 Expected Count 30.5 35.1 46.5 29.5 13.4 155.0 % within method 14.8% 17.4% 34.2% 21.3% 12.3% 100.0% Total Count 59 68 90 57 26 300 Expected Count 59.0 68.0 90.0 57.0 26.0 300.0 % within method 19.7% 22.7% 30.0% 19.0% 8.7% 100.0%\fChi-Square Tests Asymptotic Significance Value df (2-sided) Pearson Chi-Square 15.566 049 Likelihood Ratio 15.826 045 N of Valid Cases 300 a. 1 cells (6.7%) have expected count less than 5. The minimum expected count is 3.99