 Statistics Questions

Subject Mathematics General Statistics

Question

1. See the following data:
Time Method
6 OnLine
7.1 OnLine
5.9 OnLine
8.9 OnLine
7.3 OnLine
6.1 OnLine
7.7 OnLine
7.1 OnLine
6.3 OnLine
8.4 OnLine
7.9 OnLine
6.9 OnLine
6.9 OnLine
6.3 OnLine
6.7 OnLine
6 OnLine
6.4 OnLine
8.3 OnLine
7.5 OnLine
8.2 OnLine
5.3 Half&Half
6.2 Half&Half
8.4 Half&Half
8.2 Half&Half
7.4 Half&Half
8.2 Half&Half
7.9 Half&Half
5 Half&Half
7.1 Half&Half
6.5 Half&Half
7.7 Half&Half
5.3 Half&Half
6.1 Half&Half
7.2 Half&Half
7.2 Half&Half
6 Half&Half
6.1 Half&Half
7 Half&Half
7.7 Half&Half
7.2 Half&Half
5.7 LecturePlus
5.5 LecturePlus
7 LecturePlus
5.9 LecturePlus
4.1 LecturePlus
7.1 LecturePlus
6.6 LecturePlus
6.4 LecturePlus
5.4 LecturePlus
5.7 LecturePlus
6.1 LecturePlus
4.8 LecturePlus
7.2 LecturePlus
6.2 LecturePlus
4.9 LecturePlus
6.3 LecturePlus
5.4 LecturePlus
6.3 LecturePlus
6.1 LecturePlus
5.5 LecturePlus
5.3 Lecture
5.1 Lecture
6.6 Lecture
6.4 Lecture
4.9 Lecture
7.3 Lecture
5.6 Lecture
6.5 Lecture
6.2 Lecture
4.8 Lecture
7.1 Lecture
7.1 Lecture
5.8 Lecture
5.9 Lecture
5.9 Lecture
5.7 Lecture
7.3 Lecture
5.2 Lecture
5.9 Lecture
6.4 Lecture

Suppose that a MBA level stat course is taught using four different methods of instruction: (1) 100% online; (2) a “half and half” format where one week the class meets for a lecture, the next week, material is posted online, etc.; (3) traditional weekly lecture meetings plus supplementary material posted online; and (4) traditional weekly lecture meeting with no use of the web.
Twenty students are surveyed from each course and are asked to estimate the average number of hours per week that they spent on the course, including time spent attending lectures if the course had any. The results appear in the included data file.

(a) Create boxplots for these four sets of data (all on the same graph). Based on the plots, what do you think about the ANOVA assumptions of normal populations and equal variances? (You’ll test these in Part (d), I’m just interested in a visual interpretation here.) Your answer should include justification..... don’t just say ‘yup’ or ‘nope.’

(b) Create interval plots for this data (four intervals on the same plot) so that we can visually compare the four groups. This is the plot that shows a confidence interval for each unknown population mean. Based on the plot, do you believe that the population mean time spent is the same for all groups? Again, show the reasoning behind your answer.

(c) Let μ1 represent the population mean time spent for method (1), μ2 the mean time spent for method (2), and so on. Test the null hypothesis that all means are equal at the 0.05 level of significance.

(d) Is there evidence of violations of the usual ANOVA assumptions of equal variances and normal populations? Set up and perform appropriate TESTS at the α = 0.05 level of significance.

(e) If your answer in Part (c) was to “reject H0” then perform an appropriate statistical procedure to determine which means are different from which other means (a visual inspection is not sufficient.). If differences exist, be sure to report the ‘direction’ of the differences!

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