Final Project (Download link : HERE)
Student
|
Sex
|
Pre-test
|
Post-test
|
Hours
per week studying statistics
|
Matilda
|
F
|
4
|
6
|
15
|
Franklin
|
M
|
2
|
5
|
18
|
Lily
|
F
|
4
|
7
|
13
|
Paul
|
M
|
3
|
6
|
11
|
Louise
|
F
|
5
|
5
|
7
|
Golda
|
F
|
4
|
6
|
12
|
Duncan
|
M
|
2
|
5
|
14
|
Philip
|
M
|
6
|
7
|
9
|
There is a limited
amount of data presented here because I don't want to overwhelm you with long calculations. Please assume that the distribution is
normal.
Answer
the following questions about this problem.
Preliminary
information about the data (36 points):
Points
|
Question
|
3
points
|
1.
What is the head of the statistics department trying to find out?
|
4points
|
2.
What are the data elements (variables) that are being collected by the
researcher?
|
4
points
|
3.
What is the measurement scale of the each of the variables of interest?
|
2
points
|
4.
What is the mean of the pre-test scores?
|
2
points
|
5.
What is the median of the post-test scores?
|
2
points
|
6.
In both the pre and post test conditions, considering these as a single
sample, what is the mode? (There should be 16 values considered.)
|
2
points
|
7.
What is the range of the hours studied values?
|
3
points
|
8.
Can you calculate a mean for the sex of the students involved in this pilot
study? Explain your answer.
|
6
points
|
9.
What is the standard deviation of the pre-test scores? Please show all your work. You don't have
to do the standard deviation of the post-test scores.
|
3
points
|
10.
Looking at the pre-test is the distribution of these scores normal? Demonstrate this with a stem and leaf plot
(you'll need to look this up on the web).
|
5
points
|
11.
State the percentages of the empirical rule.
|
First
statistical test (29 points):
Points
|
Question
|
2
points
|
12.
What statistical test are you going to use to find out whether there is a
significant difference between the pre-test sample and the post-test
sample? Be specific.
|
3
points
|
13.
Explain why this test is appropriate. Include
in your answer three of the
assumptions of the test you're proposing and explain why each is important.
|
2
points
|
14.
What is the null hypothesis?
|
2
points
|
15.
What is the research hypothesis?
|
5
points
|
16.
Perform the calculations for your proposed statistical test and show your
work and your answer.
|
2
points
|
17.
What is your observed value?
|
2
points
|
18.
What are your degrees of freedom?
|
2
points
|
19.
Is this a one-tailed or two-tailed test?
|
2
points
|
20.
What table are you going to use to find your critical value? Please be specific and give the page number
from Aron, Coups and Aron.
|
2
points
|
21.
What is your critical value? Your p value should be .05.
|
2
points
|
22.
Based on your observed and critical values, is the difference between these
two groups significant?
|
3
points
|
23.
What conclusion can you draw from your result? State your conclusion in
words, based on your null hypothesis.
|
Second
statistical test (16 points):
In your first statistical test you
tried to find out whether or not there was a difference between two groups of
test scores, the pre-test and the post-test. What if we wanted to
find out if there was a difference between the pre- and post- test scores broken
down by sex?
Points
|
Questions
|
4
points
|
24.
How many groups are there for this analysis considering pre-test data,
post-test data and sex? Name them.
|
2
points
|
25.
What statistical test would propose to find out if there is a difference
between these groups?
|
2
points
|
26.
What would your null hypothesis be for this additional analysis?
|
2
points
|
27.
What would your research hypothesis be for this additional analysis?
|
2
points
|
28.
In general, what conclusion could you draw from that statistical test?
|
2
points
|
29.
In general, what conclusion can't you draw from this statistical test?
|
2
points
|
30.
What additional statistical test do you need to perform in order to find out
where the actual difference lies?
|
Third statistical test (15 points):
In your first and second statistical
tests you were trying to find out whether there was a difference between the
way various groups performed on the SAME variable. In this third scenario
we want to find out whether there is a relationship between TWO different
variables.
Points
|
Questions
|
2
points
|
31.
What statistical test do you propose to find out the relationship between
post-test scores and the number of hours studied?
|
3
points
|
32. What formula would you use to find the
relationship between the post-test scores and the number of hours studied?
|
4
points
|
33. Using this formula, what would your result
be?
|
2
points
|
34. How would you interpret your result?
|
2
points
|
35.
In general, what can you conclude from this statistical test?
|
2
points
|
36.
In general, what can't you conclude from this statistical test?
|
Fourth
statistical test (4 points):
Now, based on the result of the third test, we can conduct a further
statistical test in order to see if we can make a suggestion to students about
the number of hours they need to study in order to learn the most in their
statistics course.
Points
|
Question
|
2
points
|
37.
What statistical test can we use to predict the number of hours a student
needs to study in order to do well in statistics?
|
2
points
|
38. Describe in words the interpretation you
would be able to make based on this additional statistical test?
|
