Question 01:

“How would you describe the performance of the students over the three quizzes? Specifically, is there an average improvement of Quiz 2 over Quiz 1 and of Quiz 3 over Quiz 2?”

– Using boxplots to visualize the data, we clearly see that the overall Quiz Grades do improve from Quiz 1 to Quiz 2. And from Quiz 2 to Quiz 3.

## 
##  One Sample t-test
## 
## data:  Quiz.2
## t = 3.4588, df = 37, p-value = 0.001382
## alternative hypothesis: true mean is not equal to 4.105263
## 95 percent confidence interval:
##  4.377757 5.148558
## sample estimates:
## mean of x 
##  4.763158
## [1] "We can see that given the T-test, the true mean of Quiz 2 is not equal to that of Quiz 1."
## 
##  One Sample t-test
## 
## data:  Quiz.3
## t = 5.5456, df = 37, p-value = 2.59e-06
## alternative hypothesis: true mean is not equal to 4.763158
## 95 percent confidence interval:
##  5.748507 6.883072
## sample estimates:
## mean of x 
##  6.315789
## [1] "We can see that given the T-test, the true mean of Quiz 3 is not equal to that of Quiz 2."

Question 02:

  1. “Does the section make a difference when it comes to average performance in each of the quizzes?”

– Again, we visualize the data with boxplots. We can clearly see that for Quiz 1 (a), Section B does a lot better than Sections A and C, who perform more or less the same. For Quiz 2 (b), Section C does better than Section A, and Section A does better than Section B. For Quiz 3 (c), Section B does better, again. While Section C does better than Section A. On Quiz 3, Section A has a larger spread than any other section throughout the three quizzes.

  1. “Does the sex of the student make a difference when it comes to average performance in each of the quizzes?”

– For Quiz 1 (d), we can see that the median scores for Females and Males are pretty much the same, however, since Females have a bigger upper spread, their mean is expected to be higher than Males. For Quiz 2 (e), we see a similar case, the median and low quartile values are pretty much the same for both sexes, however, Females on the upper quartile score higher, moving their average above Males. For Quiz 3 (f), Females clearly score higher than males, therefore, Sex does matter. It can be said that from Quiz 2 to Quiz 3, Females improved by a higher factor than males. Both sexes improved on each Quiz.

Question 03:

“Does the section and sex make a difference when it comes to average performance over Quizzes 1, 2 and 3?”

– Section and Sex make a clear difference when we visualize the mean quiz grade throughout the three quizzes. We see that Females do a lot better than Males in Sections A and B. And Section A does better overall, than Sections C and A (worst).