As shown in several lectures there are two distinct methods of calculating summary or descriptive statistics using Excel.
statistics
Description
Final_exam = 2.05
+ 1.8Tutorial_ attend
(1.7) (0.45)
Figures in parentheses represent standard errors
No. of observations 737, Rsquared 0.29. (These results are illustrative
only- i.e. I made them up.)
Then you would interpret and carry out relevant hypothesis tests.
Problem Description:
You have been appointed by the Dean of Business to
analyse student performance in a course offered by a Business School. The focus
is upon the key determinants of the Final_exam (i.e. the students’ final exam mark),
in particular the role of the Assignment (i.e. Assignment_grade) and Tutorial_attend
(i.e. the number of tutorials attended during the semester). Using the tools
learned in your current Business Statistics course provide the Dean with an
analysis of Final_exam performance.
1.
As shown in
several lectures there are two distinct methods of calculating summary or
descriptive statistics using Excel. This question requires you to use both
methods. First use Excel Data Analysis Tool Pack (the descriptive statistics
option) to calculate summary statistics for all variables included in the attached
data file. Comment on your summary statistics including any differences across
the 3 included variables, i.e. Final_exam, Assignment_mark and Tutorial_attend.
Carefully interpret. Second use excel to
calculate all descriptive statistics documented in your report. These
calculations should be carefully laid out in excel and should use excel formula
NOT Data Analysis Toolpack. [Topic 1]
2.
Use
appropriate graphs to interpret the relationship between (i) Final_exam and assignment_grade;
(ii) Final_exam and Tutorial_attend; and (iii) assignment_grade and Tutorial_ attend. Carefully interpret
and explain. [Topics 1]
3.
Calculate
the sample correlation and covariance for the above 3
relationships in question 2. Carefully interpret your results. Once again use Excel
for these calculations using both methods i.e. Data Analysis Tool Pack (options
covariance, correlation) and using Excel formulae without use of Data Analysis
Tool Pack. (Hint- if you find a discrepancy in your answers between the 2 excel
methods can you explain why?)
4.
For
this question ONLY, assume that the first 26 observations are male (i.e.
rows 2-27 of the original data) and the last 29 observations are female. Use
Excel both with and without Data Analysis Tool Pack to test the null hypothesis
that the mean of the Final_exam is equal for males and females. Interpret your results.
[Topics 6-8]. Do not include
analysis by gender in any further parts of the analysis i.e. questions 5, 6 and
7.
5.
Use simple
regression to explore the relationship between (i) Final_exam (Y) and
assignment_grade (X); (ii) Final_exam (Y) and Tutorial_attend (X). Carry out
any relevant hypothesis tests using a two-tailed hypothesis test approach at
the 5% significance level. You may use Data Analysis Tool Pack for this. Carefully
interpret and explain. [Topics 9-10]
6.
Now use multiple regression to explore the
relationship between Final_exam (Y), assignment_grade (X1)
and Tutorial_attend (X2). You may use Data Analysis Tool Pack for this. Carry
out any relevant two-tailed hypothesis tests at the 5% significance level.
Carefully interpret. If you had a magic wand and could request additional data
for your analysis of this course, what extra variables would you request and
why? [Topic 10-11]
7.
Using your
multiple regression results to predict Final_exam for a student with the mean assignment_grade
and tutorial_attend equal to (i) 2 tutorials, (ii) 3, (iii) 4 and (iv) 5 tutorials.
(Hint this means you will have 4 distinct predictions for Final_exam) Carefully
interpret your results.
