MAST10010: Data Analysis 1 Assignment 2
Due Date: Monday October 12th, 12 noon.
• You must submit an electronic copy of your assignment via the Canvas (GRade- Scope).
• Clearly label your assignment with your name and student ID number, your tutors name, and your tutorial group (day and time). Where possible, please submit your answers as a word processed document (you may leave gaps to hand-write sym- bols and equations, if necessary).
• Deadlines for handing in your assignments are enforced and late assignments will not be accepted unless there are extenuating circumstances. You must talk to the lec- turer (Dr Julia Polak) personally about late assignments. Individual tutors have no discretion to accept late assignments.
This assignment consists of three (3) questions worth a total of 40 marks. It contributes 5% towards your final grade.
Instructions
Software:
You must use Minitab to produce any graphs, tables and descriptive statistics. You may use Minitab to check your own calculations, but do not include Minitab output unless specifically requested.
Graphs:
• must include your name/student number, which can be added by right-clicking the graph and selecting Add → Footnote or Add → Subtitle.
• should be clear: ensure that labels and titles are correct and appropriate; you can add gridlines/change symbols/colour as appropriate to make the graph clearer. There are some marks awarded for improving upon the default from Minitab.
Statistics:
must be relevant: you will be penalised for including statistics which are not relevant to the questions asked.
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Comments:
• must be in the context of the data.
• should be supported by relevant statistics where possible.
• should be concise and informative. You may use dot-points.
Do Videogames improve Eyesight?
For questions 1 and 2 you will need to access the data file 2020 Asst2 (file can be downloaded from the Assignments link as a Minitab worksheet and also as an Excel file).
The Variables:
Question 1: Does playing a videogame help those with Amblyopia?
[1 + 6 + 2 = 9 marks]
This question is based on simulated data for the study by S.T. Jeon et al. (2012) ‘The
Effect of Video Game Training on the Vision of Adults with Bilateral Deprivation Ambly-
opia’, Seeing and Perceiving, which you can read about here: https://www.telegraph.co.uk/news/science/science-news/9088262/Playing-video-games-improves- eyesight.html (also linked on the Assignments page of the LMS).
You DO NOT need the information from either of these articles to answer the questions; they are provided for interest only.
Amblyopia (childhood cataracts) are an eye problem, present from a young age, which can be corrected using surgery and special contact lenses. However, their eyesight continues to function below average. The contrast sensitivity for each participant was measured before beginning the videogame training; they spent 40 hours playing ‘Medal of Honor’ over a one-month period; and their contrast sensitivity was measured again. A higher value for contrast sensitivity represents better eyesight.
(a) Explain why these data are paired.
(b) Conduct a hypothesis test to determine whether there was an improvement in the participants’ eyesight. You should use a significance level of α = 0.01 for this test. You must show all calculations (do not include Minitab output, but you may use Minitab to obtain summary statistics).
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Column
Name
C1 C2
Pre Post
Contrast sensitivity scores for amblyopia patients at the start of the study. Contrast sensitivity scores for amblyopia patients at the end of the study.
C3 C4
AVG NAVG
Contrast sensitivity scores for action videogame players Contrast sensitivity scores for non-action videogame players
Your answer needs to include (5 step process meets these requirements):
• A clear statement of the hypotheses in terms of the parameter(s) of interest.
• Calculate se(estimator).
• Calculate the test statistic, and give its distribution under the null hypothesis.
• Give a range for the P-value for the test, using the tables in the Problem Booklet.
• State your conclusion in the context of the data.
(c) Researchers have decided that it would be useful to detect an improvement of 0.1 units in contrast sensitivity, with a 0.01 significance level. Assuming that the sample standard deviation sdiff = 0.22, use Minitab to find the sample size required to have a power of 0.9. Include your graph and your final answer.
Question 2: Does playing action videogames improve the eyesight of healthy individuals?
[2 + 2 + 4 + 3 + 4 + 1 + 1 = 17 marks]
This question is based on simulated data for the study by R. Li et al. (2009) ‘Enhancing the contrast sensitivity function through action video game training’, Nature Neuroscience, Vol. 12(5), 549–551 which you can obtain from the Library website (online Journal search). You DO NOT need information from this article to answer the questions; it is provided for interest only.
Researchers recruited 22 healthy individuals (contrast sensitivity in the normal range) between the ages of 20–25, who did not play videogames. They were randomly allocated to play either action videogames1 (AVG) or non-action videogames2 (NAVG) for 50 hours over a period of 9 weeks. As with question 1, the variable of interest is the contrast sensitivity (higher scores represent better eyesight).
(a) Explain why non-action videogames was chosen as the second treatment, rather than doing nothing.
(b) Produce an appropriate graph showing contrast sensitivity for both groups.
(c) Comment on the effect of Type of Videogame on Contrast Sensitivity. You should support your comments with relevant statistics, but do not include Minitab output. Your comments must be less than 100 words.
(d) Calculate a 95% Confidence Interval for the difference in mean contrast sensitivity for the two groups. Show all of your calculations (do not include Minitab output, but you may use Minitab to obtain summary statistics).
(e) What assumptions have you made in calculating this interval? Were they satisfied? (You need to provide evidence, in the form of one graph and a calculation.)
1Unreal Tournament 2004 (Atari) and Call of Duty 2 (Activision). 2The Sims 2 (EA Games).
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(f) Without doing further calculation, would a test of the hypotheses H0 : μ1 − μ2 = 0 and H1 : μ1 − μ2 ̸= 0 be significant at the α = 0.05 level? Explain briefly.
(g) Does this study provide evidence of a causal relationship? Why/why not?
Question 3: University students and climate change.
[5 + 2 + 2 + 3 = 12 marks]
When asked to nominate the issue they believe politicians need to act on most urgently, 10% of Australians respond “Climate change” (you may assume this is the true population value). A small study3 conducted by UMSU (the University of Melbourne Student Union) found that out of 30 students, 7 nominated that climate change is the most pressing issue.
(a) Conduct an approximate Hypothesis Test (using α = 0.05) to determine if there is a difference between students at the University of Melbourne and the Australian population. Show all of your calculations and steps.
Your answer needs to (the 5 step process meets these requirements):
• State the hypotheses in terms of the parameter(s) of interest.
• Calculate sd(estimator).
• Calculate the test statistic, and give its distribution under the null hypothesis. • Give the P-value for the test, using the tables in the Problem Booklet.
• State your conclusion in the context of the data.
(b) Use Minitab to perform an exact Hypothesis Test to determine if there is a difference between students at the University of Melbourne and the Australian population. You only need to provide the Minitab output and a conclusion (in context).
(c) Explain why there is such a large difference between the P-values for the tests you performed in (a) and (b). You may include an additional calculation, but this is not required.
(d) Based on the evidence available, it is believed that the proportion of University of Melbourne students who nominate climate change as the most urgent issue is no more than 30%. Researchers would like to estimate the proportion using a 90% confidence interval based on a normal approximation, with a maximum margin of error of 0.02. What sample size would be required to achieve this? Show your calculations as well as your answer.
Relevance [2 marks]
You don’t need to do anything to get these marks. They will be deducted if you include anything (including, but not limited to graphs and Minitab output) that is not specifically requested in any question.
3This is a fictitious study.
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