Duncan et al. (2012) report a study which explores the effect on course grade of cell phone use during class. As part of the study, students in five University of Colorado Astronomy classes self-reported their cell phone usage per one hour class. Students were then classified by their cell phone use into four groups: Never, 1-2, 3-4, and >5 times per class. The grades of the students were recorded on a four point scale with an 'A' being 4.0. Suppose the grades from one of the five classes were as tabulated below:



Duncan, D., Hoekstra, A. and Wilcox, B. (2012): Digital devices, distraction, and student performance: does in-class cell phone use reduce learning? Astronomy Education Review 11, 010108-1, 10.3847/AER2012

Part a)
In the article, the authors display their data using a plot of means with error bars. Which of the following would have been a preferable method?

A. Side-by-side boxplots
B. A histogram
C. A pie chart
D. Four histograms plotted on the same axis
E. Four stem-and-leaf plots


Part b)
Which of the following hypotheses could reasonably be tested by the data presented in the study?

A. In the four groups of students determined by their cell phone use in class, the sample means of the course grades are equal.
B. In the four groups of students determined by their cell phone use in class, the sample variances of the course grades are equal.
C. In the population of students who take an Astronomy class at the University of Colorado, if placed into four groups determined by their cell phone use in class as above, the means of the course grades are equal.
D. There is no correlation between course grade and the number of times students use their cell phone in class.
E. In the population of students who take an Astronomy class at the University of Colorado, if placed into four groups determined by their cell phone use in class as above, the variances of the course grades are equal.


Part c)
Perform a suitable nonparametric test in R on the data above. Provide the value of your test statistic to two decimal places.


Part d)
Under the null hypothesis, the statistic should be an observation from which probability distribution?

A. The Chi-squared distribution on four degrees of freedom.
B. The standard Normal distribution.
C. The Chi-squared distribution on two degrees of freedom.
D. The t distribution on two degrees of freedom.
E. The Chi-squared distribution on three degrees of freedom.
F. The $F_{3,36}$ distribution.


Part e)
Would you reject or not reject your null hypothesis at the 5 % significance level?

A. Not reject
B. Reject