Question

13a. Normally psychology majors have the following grade distribution in Elementary Statistics: 30%-A’s, 40%-B’s, 20%-C’, 10%-D’s and 0%-F’s. This semester, out 200 students 50 had A’s, 80 had B’s, 60 had C’s, and 10 had D’s. There were no F’s. At a one percent significance level, test the null hypothesis that this semester’s grade distribution has significantly changed from the norm. Please show work.

Answer 1

H0: this semester’s grade distribution is same with the norm

H1: this semester’s grade distribution has significantly changed from the norm

Expected percentages are= 30,40,20,10

Observed percentages are =25,40,30,5(convering the proportion to percentage)

Test statistic, chi square(​​​​​​) =

(observed - expected) ^2 /expected

=(30-25) ^2 /30+...

=25/30+0+100/20+25/10

= 8.33

Critical value for 1 % singnificance level and dof =(5-1)=4 is 13.277

Since critical value is greater than test statistic, so we fail to reject null hypothesis. We can say this semester’s grade distribution is same with the normal.

Please support me by putting thumbs up. Thank you.