Notes • Use automated RStudio routines to produce the output need to answer the questions. • Report (copy/paste) your RStudio output from the console to

Notes • Use automated RStudio routines to produce the output need to answer the questions. • Report (copy/paste) your RStudio output from the console to support your answers. • There is no need to check your answers by manual (formula-based) calculation, but you can if you wish (and this might give you partial credit if your RStudio output/command is incorrect). • Include your R code at the end of your assignment; failure to include this (or substantial parts of it) may incur a penalty of up to five marks. • Conduct all hypothesis tests at the 5% level of significance unless otherwise stated. • When writing up conclusions from hypothesis-testing results, answer in the context of what’s being investigated, not merely in terms of whether the null is rejected or not. • Where asked for critical values, use RStudio and report the commands used. Image transcription text Data description and background
(data file: marks.csv)
A researcher obtained data on 400 BCom students’ recent exam marks on level-1 and level-2
statistics subjects. (The level-1 subject is the main prerequisite for the level-2 subject; think
of introductory and intermediate statistics.) On the level-2 course, students were allowed to
complete their assignments in groups of up to two (i.e., pairs) or individually (alone). Of the
400 students, half (200) completed their assignments in groups of two (pairs) and the other
half (200) completed their assignments alone. The researcher is primarily interested in
whether assignment-pairing students performed better in the level-2 exam than students who
did their assignments individually (i.e., assignment-nonpairing students). The data file
contains information on the variables listed below.
XNGi:
level-2 exam mark for assignment-nonpairing student i;
XGi:
level-2 exam mark for assignment-pairing student i;
PXNG:: level-1 (prerequisite) exam mark for assignment-nonpairing student i;
PXGi: level-1 (prerequisite) exam mark for assignment-pairing student i;
The researcher includes the level-1 (prerequisite) exam marks data to investigate whether
students who did well in the prerequisite-subject’s exam also did well on the level-2 exam (as
one would expect).
All exam marks are out of 100.
Note: no tests of normality are needed because we have 200 observations on both assignment-
pairing and nonpairing students. (See lecture 2.) Image transcription text Question 1
(15 marks; 5 per part)
Here, we investigate whether the variances of assignment-pairing students’ level-2 exam marks
and assignment-nonpairing students’ level-2 exam marks differ.
(a) Specify suitable null and alternative hypotheses for the test and define your notation.
(b) Compute an appropriate test statistic and report appropriate critical value(s) for the test
(latter just for practice!).
(c) Based on the p-value from the RStudio output, what do you conclude?
Question 2
(15 marks; 5 per part)
Here, we investigate whether assignment-pairing level-2 students average higher level-2 exam
marks than assignment-nonpairing students.
(a) Specify suitable null and alternative hypotheses for the test and define your notation.
(b) Taking account of your result from question 1, compute the p-value for testing the
hypotheses specified in part (a) of this question.
(c) What do you conclude?
Question 3
(15 marks)
In this question, we use data on assignment-pairing students only to investigate whether there
is evidence that above-average performers on the level-1 exam do better in the level-2 exam
(as one would expect). To do this, follow the instructions below.
. Use only the data on the students who paired for assignments.
Create two new data frames: one for assignment-pairing students whose level-1 exam mark
is above the median (among assignment-pairing students) and one for assignment-pairing
students whose level-1 exam mark is below the median. (Note that there are 98 students in
the former category and 99 students in the latter category; three have the median mark.)
Call these two groups ‘quant-skilled’ (QS) and ‘quant-unskilled’ (QU), respectively.
Having done the above in RStudio (tutorial 1 should ), perform the test described
below, and explain what conclusion you draw from the p-value for the test.
Test whether (assignment-pairing) QS students do better (on average) on the level-2 exam
than do (assignment-pairing) QU students. (Assume unequal population variances for this
test.) 70 65 73 81 94 83 40 82 62 49 74 70 84 83 89 44 36 59 54 83 79 76 76 88 78 47 85 79 61 92 89 83 65 66 55 89 79 81 88 63 60 79 82 96 91 81 81 100 85 77 73 93 13 91 56 73 81 56 73 98 93 47 93 89 92 92 56 35 65 76 71 84 52 62 87 57 55 78 88 73 80 85 82 71 64 86 84 70 74 77 61 53 77 52 82 56 61 73 67 54 92 57 34 87 71 43 79 73 44 82 84 80 88 64 49 53 70 49 87 65 54 43 78 71 81 82 78 82 93 74 75 53 59 73 55 66 66 78 58 87 59 85 65 92 75 93 73 62 88 83 60 97 52 87 56 83 34 66 66 50 70 59 64 55 64 50 80 76 44 92 81 61 86 70 65 85 87 86 76 90 88 87 83 62 64 81 84 84 72 89 72 94 73 94 83 92 51 84 94 63 98 75 85 87 91 83 80 87 61 85 90 79 69 60 79 62 64 87 84 73 76 59 91 71 76 62 74 79 55 89 71 91 77 97 85 72 73 64 88 80 96 86 90 61 79 94 77 80 89 66 68 63 68 85 85 82 87 69 93 96 98 89 85 84 66 83 83 84 92 87 85 84 86 79 67 82 76 90 78 78 56 52 87 100 85 70 82 91 93 96 92 87 57 84 89 81 90 82 88 91 74 82 72 85 70 76 85 74 89 84 92 80 74 82 74 97 82 94 65 80 58 51 94 82 84 64 88 98 74 91 82 88 92 72 70 85 71 88 76 66 70 67 86 89 93 94 93 91 84 56 86 72 58 86 50 48 71 79 36 92 54 41 57 84 75 69 70 58 75 86 59 95 80 61 87 89 54 76 68 84 76 89 61 82 59 44 79 84 90 90 87 78 90 79 31 78 91 41 92 59 58 75 76 38 80 63 34 77 73 81 82 79 38 73 68 74 69 50 57 61 49 65 77 95 61 98 92 51 80 53 52 70 82 44 86 82 44 76 51 64 76 71 45 92 75 80 73 65 61 76 84 47 82 83 56 94 84 78 89 77 61 83 81 71 54 86 57 84 49 44 66 88 53 93 82 86 94 93 76 86 96 65 88 77 77 80 70 84 77 67 65 82 58 84 72 92 62 87 94 78 83 80 94 84 74 85 78 97 65 78 88 67 82 86 80 86 82 94 90 69 90 87 79 88 63 85 61 56 61 69 60 85 67 84 50 53 69 95 61 86 60 49 70 60 56 81 68 82 84 64 74 82 82 66 64 80 82 84 54 74 38 61 83 79 90 36 88 86 83 64 89 76 78 72 47 70 81 61 77 84 83 80 78 55 84 76 81 90 76 60 70 89 96 72 66 35 76 86 71 81