HOMEWORK #11
Computations You Should be
Able to Perform.
Problem 1. An
experimenter wanted to decide if maze learning in rats required the animals to
actually walk or run through the maze.
The experimenter took two randomized groups or hungry rats. The groups of ten rats each were
"trained" in
a maze in which food was available in the goal box.
One group was permitted to run or walk through the maze. Rats in the other group were placed in a
small cart that was pulled through the maze by the experimenter. Both groups were then given five
non-reinforced test trials where they were permitted to run or walk through the
maze freely.
|
|
N |
Mean |
S |
S2 |
SS |
|
Walk |
10 |
10.9 |
1.20 |
1.44 |
12.96 |
|
Cart |
10 |
13.5 |
1.58 |
2.496 |
22.4676 |
|
1. What is your research hypothesis? |
There is
a difference in time between walking and riding. |
|
2. What is Ho? |
Walking or riding through
a maze does not influence learning time.
(Mean walking = mean riding.) |
|
3. What is H1? |
There is a difference in
learning time based on whether rats walk or ride. (Mean walking ≠ mean
riding) |
|
4. What is the statistical test and df? |
Independent samples
t-test. df =
N-2 = 20-2 = 18 |
|
5. What is the
significance level and its critical value? |
Two-tailed
test. P <
.05, cv = 2.101 P< .01, cv
= 2.878 |
|
6. What is your best estimate of the
population σ2 |
Pooled population variance
estimate = 1.9682 |
|
7. What is the Standard error of the
mean? |
.6274 |
|
8. What is your calculated statistic? |
t(18)
-4.144 |
|
9. What is your statistical decision? |
Reject
the null hypothesis |
|
10. What is your conclusion? |
The
walking group got through the maze significantly faster. Walking leads to faster learning. |
|
11. What is the effect size? |
.488 |
Problem 2. A
statistics professor wanted to know if it was better to teach students by
giving examples first, then explaining the theory or if was better to give the
theory first and then give examples. The
researcher collected data from two groups of subjects of randomly chosen
subjects. Their results on a statistics
test are summarized below. Can the
researcher conclude that one teaching strategy was more effective than the
other? If “Yes” which one is more
effective?
|
|
N |
Mean |
S |
S2 |
SS |
|
Examples First |
18 |
18.6 |
1.38 |
1.904 |
32.375 |
|
Theory First |
14 |
17.3 |
1.414 |
2.00 |
26.00 |
|
1. What is your research hypothesis? |
Students who are given examples
first will score differently on a statistics test than students who are given
theory first. |
|
2. What is Ho? |
There will be no
difference between the test scores of the students who are taught when given
the theory first or given examples first.
MeanEXAMPLES = MeanTHEORY |
|
3. What is H1? |
Students who are given
examples first will score differently on a statistics test than students who
are given theory first. MeanEXAMPLES
≠ MeanTHEORY |
|
4. What is the statistical test and df? |
Independent samples
t-test. df = 18+14-2=30 |
|
5. What is the
significance level and its critical value? |
Two
tailed test p < .05 cv
= 2.042 |
|
6. What is your best estimate of the
population σ2 |
Pooled
variance estimate = 1.946 |
|
7. What is the Standard error of the
mean? |
.497 |
|
8. What is your calculated statistic? |
t(30) = 2.616 |
|
9. What is your statistical decision? |
Reject the null hypothesis |
|
10. What is your conclusion? |
Giving examples first is more
effective than giving theory first. |
|
11. What is the effect size? |
.186 |
Problem 6. Pat A.
Kayke wanted to know if people who said a prayer just
before answering quiz questions did better on quizzes. A sample of 6 students alternatively prayed
and did not pray during a statistics quiz.
Their scores are reported below.
Did the prayer have an effect?
|
Subject |
Prayer |
No Prayer |
Difference |
(D – MeanD)2 |
|
A |
93 |
98 |
5 |
4.696 |
|
B |
90 |
94 |
4 |
1.362 |
|
C |
95 |
96 |
1 |
3.36 |
|
D |
92 |
91 |
-1 |
14.692 |
|
E |
95 |
97 |
2 |
.694 |
|
F |
91 |
97 |
6 |
10.03 |
|
|
MeanD
=2.8333 |
SS =
34.834 S2
= 6.9668 |
||
|
1. What is your research hypothesis? |
People who say prayers
will do better on quizzes. |
|
2. What is Ho? |
People who say prayers
won’t do better on quizzes. |
|
3. What is H1? |
People who say prayers
will do better on quizzes. |
|
4. What is the statistical test and df? |
Within groups t-test: df = N-1 = 5 |
|
5. What is the
significance level and its critical value? |
One
tailed test. Critical value p<.05 =
2.015 |
|
6. What is your best estimate of the
population σ? Why did I divide by 6-1? |
SQRT(34.834/6-1)
= 2.6395 |
|
7. What is the Standard error of the
mean? |
2.6395/SQRT(6)
= 1.0776 (This
computation uses s as the numerator.) Or SQRT(6.9668/6)
= 1.0777 (This is
the one I showed in class) |
|
8. What is your calculated statistic? |
t(5) = 2.833/1.0777
= 2.629 |
|
9. What is your statistical decision? |
Fail to reject the null
hypothesis. |
|
10. What is your conclusion? |
The opposite was found to be
true; when students did not pray their scores were better. (Note: it is
important to keep track of which mean is larger otherwise you may
misinterpret the significance test.) |