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STAT 300 – Fall 2016 – Assignment

DEPARTMENT OF STATISTICS, THE UNIVERSITY OF BRITISH COLUMBIA
STAT 300 – Fall 2016 – Assignment # 2
(Answers need to be accompanied by the cover sheet provided in the course website.)
(1) (18 marks) Read the first three sections of the following article:
Ma-Kellams, C. and Blascovich, J. (2012): Enjoying life in the face of death: East–West differences in responses to mortality salience. Journal of Person-ality and Social Psychology, No.5, 773-786
Describe briefly but clearly the motivation for the study. Describe what you can about the experimental conditions in the study. Define clearly the response variable. Is Figure 3 in the article an informative way to display the data? Justify your thinking. Suggest a graphical approach that would have been more informative. Which effects, if any, did the researchers conclude affect the response for this study?
Perform an analysis of variance on the data provided. Summarise your conclusions clearly. List the matching learning outcomes assessed in the three parts above, for this ques-tion. (Learning Outcomes are posted in the Course Information folder.) (11 marks) A research assistant recorded the lifetimes of twenty guinea pigs who resided in a laboratory. The lifetimes in months are recorded below:
Create a graphic that illustrates the shape of the distribution of the data above. Com-ment on the shape. Applying the Central Limit Theorem, find an estimate of the standard deviation of the sample mean in this example and hence create a 95% confidence interval for the population mean. What reservations might you have about this estimate? Using the above data, create an empirical bootstrap distribution (EBD) for the mean using 200 resamples. Create a histogram to illustrate your EBD, and comment on its shape. Use your EBD to find a 95% bootstrap confidence interval for the mean. Describe your
Use your EBD to find an estimate of the standard deviation of the sample mean here. Compare your value with that used in (b). (8 marks) A researcher has a dataset comprised of scores on three exams for a group of 350 students. The exams, each of which is scored out of 100 points, test mathematical reasoning (MATH), verbal reasoning (VRBL), and general knowledge (GNRL), respectively. The scatterplots that describe the data are given in the course website.
Which of the three analyses of the data above address the question of whether MATH and VRBL scores might be associated with each other, amongst students with com-mon GNRL score? Do the data provide evidence that there is such an association, or are they consistent with a lack of association? Justify your answers. Give an estimate and 95% confidence interval for the increase in average MATH score that corresponds to a 20 point increase in VRBL score, amongst students with the same GNRL score. Also, give an estimate and 95% confidence interval for the in-crease in average VRBL score that corresponds to a 3.2 point increase in MATH score, amongst students with the same GNRL score
It turns out that the researcher also ends up fitting a fourth model, whose output is also given in the course website.
(3 marks) Complete the online midterm exam wrapper questionnaire accessed via the link given in the course website.

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