Question

whether the president's approval rating has changed over this time frame? 32 - Perform a chi-square goodness-of-fit test for the percentage distribution of a population or the probability distribution of a random variable and interpret the results. A dean wants to know whether grade distribution in a stats class is different based on modality (face-to-face vs. online). He knows that in face-to-face sections of the course, 20% get As, 30% get Bs, 25% get Cs, 10% get Ds, and 15% get Fs. The results from online sections (100 students) from the previous semester are detailed in the table below, along with the appropriate chi-square statistic. Since the chi-square statistic (0.833) is less than the critical value is there enough evidence to suggest that online grade distributions for the course are different? Expected Observed A 20 19 B 30 28 C 25 24 D 10 11 F 15 18 Total 100 100 (O-E)? / E 0.050 0.133 0.040 0.100 0.600 0.833

Answer 1

H0: Null Hypothesis: Grade distribution in a stats class is not different based on modality

HA:Alternative Hypothesis: Grade distribution in a stats class is different based on modality (Claim)

Test Statistic $\chi ^{2}$ is calculated as follows:

Grade	Observed (O)	Expected (E)	(O - E)2/E
A	19	20	0.050
B	28	30	0.133
C	24	25	0.040
D	11	10	0.100
F	18	15	0.600
Total = $\chi ^{2}$ =			0.923

Take $\alpha$ = 0.05'

df = 5 - 1 = 4

From Table, critical value of $\chi ^{2}$ = 9.488

Since calculated value of $\chi ^{2}$ = 0.923 is less than critical value of $\chi ^{2}$ = 9.488, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that grade distribution in a stats class is different based on modality.