# Stat 300 – fall 2016 – assignment

(h) List the matching learning outcomes assessed in the three parts above, for this ques-tion. (Learning Outcomes are posted in the Course Information folder.)

(2) (11 marks) A research assistant recorded the lifetimes of twenty guinea pigs who resided in a laboratory. The lifetimes in months are recorded below:

67, |
15, |
19, |
55, |
49, |
101, |
4, |
13, |
83, |
10, |

112, |
2, |
3, |
53, |
12, |
28, |
10, |
37, |
12, |
148. |

(a) Create a graphic that illustrates the shape of the distribution of the data above. Com-ment on the shape.

(b) 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?

(c) 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.

(d) Use your EBD to find a 95% bootstrap confidence interval for the mean. Describe your

steps clearly. Writing your estimate in the form (*x*¯ ¡ *a*, *x*¯ Å*b*) , comment on how your interval estimate differs from the one in (b).

(e) Use your EBD to find an estimate of the standard deviation of the sample mean here. Compare your value with that used in (b).

(3) (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.

Not knowing much about statistics, the researcher imports the data into a statistical soft-ware package, and starts pushing buttons. He ends up with the three fitted models whose output is given in the course website, but he is not sure what to make of the results.

(a) 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.

(b) 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.

(c) It turns out that the researcher also ends up fitting a fourth model, whose output is also given in the course website.

There happens to be a second group of 100 students writing these exams, and it is reasonable to regard these students as coming from the same population as the first group. In fact, the second group has already written the GNRL and VRBL tests, and the researcher has these scores. They have not yet written the MATH test though.

The Department wants to pro–actively offer remedial resources and support to stu-dents who might need extra help in preparing for the test. Describe how you think the researcher should go about identifying which students might benefit most from this support.

(4) (3 marks) Complete the online *midterm exam wrapper* questionnaire accessed via the link given in the course website.

This activity is designed to give you a chance to reflect on your midterm exam perfor-mance and, more importantly, on the effectiveness of your exam preparation. Please answer the questions sincerely. Your responses are collected to inform the instructional team (instructors & TAs) regarding students’ experiences surrounding this exam and how they can best support your learning. Summarized results will be shared with the class.

MSB-GY-BD

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