4. Now you will compare the mean final exam (FX) scores to the four teaching strategies.

(a) Obtain the summary statistics (mean, standard deviation, IQR, min, Q1, median, Q3, max, and n) of the final exam scores for each teaching strategy. Paste the summary statistics in your report. Compare the means of the four groups. Which strategy seems the best? The worst? Compare the standard deviations of the four groups. Does it appear that the assumption of equal variability is satisfied?

(b) Obtain and paste the side-by-side boxplots into your report. Comments about the shape (symmetry/skewness) of distributions. Do the plots indicate any differences in the centers and spreads among the four groups? Are there any outliers?

(c) Consider the following parameters.

C = Average final exam score for the control group

H = Average final exam score for control plus weekly homework assignments

T = Average final exam score for control plus computer tutorials

HT = Average final exam score for control plus weekly homework as well as computer tutorials

Obtain three 95% confidence intervals for H - C, T - C, and HT - C. Paste the outputs into your report. Interpret each interval. (Hint: Although a one-sided confidence interval can be obtained in R, this type of confidence interval is not discussed in STAT 151 classes. Therefore, students must use a two-sided confidence interval to answer this question).

(d) Based on your intervals in part (a), answer the following. Your answer must have enough justification. Answers such as "yes" and "no" are not acceptable.

i.Is there sufficient evidence that adding weekly homework assignments alone (in addition to lecture notes and discussion) increased the final exam marks, on average?

ii.Is there sufficient evidence that adding computer tutorials alone (in addition to lecture notes and discussion) increased the final exam marks, on average?

iii.Is there sufficient evidence that adding weekly homework assignments as well as computer tutorials (in addition to lecture notes and discussion) increased the final exam marks, on average?