Question

There are three ways a student can end up in Calculus II at Augusta University. They can either take Calculus I or place into the class via AP credit. Further, some students take Calculus I the semester immediately before Calculus II but some students wait one or more semesters between taking Calc I and Calc II. A professor has a Calculus II class with 21 students, and they look at students’ final grades and how they got into the class.

Placed via AP credit (group A)	Took Calc I the semester immediately before (group B)	Took Calc I, but not the semester immediately before (group C)
83	70	71
70	84	70
77	86	54
81	75	71
90	72	56
94	71	68
77	97	59

a. Carry out an ANOVA to see if there are any significant differences in the final grades among these three groups. Use ? = .05 to carry out the ANOVA, then use a suitably corrected alpha to do any followup tests if needed. Assume all the ANOVA assumptions (normal populations with equal variance) are satisfied.

b. A high school student coming to AU with AP credit is concerned about skipping Calculus I and wonders if they will be at a disadvantage relative to other students who take Calculus I right before taking Calculus II. Based on your analysis, is this concern warranted?

c. A student takes Calculus I in the fall and likes their professor, but this professor is not teaching Calculus II in the spring, so the student decides to wait and see if that professor is teaching the course at a later time. Based on the data, does this appear to be a sound course of action?

Answer 1

One-way ANOVA: Group A, Group B, group C

Method

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor	Levels	Values
Factor	3	Group A, Group B, group C

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	2	1269	634.62	8.46	0.003
Error	18	1350	74.98
Total	20	2619

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
8.65934	48.46%	42.74%	29.85%

Means

Factor	N	Mean	StDev	95% CI
Group A	7	81.71	8.20	(74.84, 88.59)
Group B	7	79.29	10.06	(72.41, 86.16)
group C	7	64.14	7.52	(57.27, 71.02)

Pooled StDev = 8.65934

(a)-> Here the P-value is less than level of significance (Alpha). i.e. 0.003<0.05. so we have sufficient evidence to reject null hypothesis. Hence  there are significant differences in the final grades among these three groups.

(b)-> For Group B and group C,

and,

difference between mean of group B and C = 79.29 - 64.14

= 15.15

Since 9.7247 < 15.15 , There is significant difference between group B and group C.

Hence student who skip calculus I will be at a disadvantage relative to other students who take Calculus I right before taking Calculus II.

(c)-> It is not necessary to teach the both calculus I & calculus II by same teacher But it will be easy for the students.

so, this doesn't appear to be a sound course of action.