New England College Week6 Statistics for Social Sciences Problem Set

Problem Set 61. In an experiment designed to determine the effect of mood on perception of pain, subjects
were induced to experience a good mood, a bad mood, or had no mood induction. Participants
were then asked to rate the amount of pain they were currently experiencing. Below is a list of
the pain ratings. Test the null hypothesis that mood has no effect on perception of pain. (35
points)
Negative Mood
Positive Mood
Control Group
10
6
11
12
8
2
2
7
5
1
5
6
4
5
7
Research Problem:
Statistical Hypotheses:
Decision Rule:
Use Jamovi to calculate the F value and post hoc tests if warranted. Copy and paste your
outputs here or upload a separate file with your outputs to the assignment in Blackboard.
Decision:
Interpretation:
1
2. In a study of group productivity, participants worked alone or shared the responsibility
for building widgets with one other, with three others, or with fifteen others. Below, are
the data showing the number of widgets each group produced. Test the null hypothesis
that group size had no effect on productivity. (35 points)
Alone
Two-person
group
Four-person
group
8
6
5
6
4
6
3
6
9
10
12
9
Sixteen-person
group
5
8
3
6
Research Problem:
Statistical Hypotheses:
Decision Rule:
Use Jamovi to calculate the F value and post hoc tests if warranted. Copy and paste your
outputs here or upload a separate file with your outputs to the assignment in Blackboard.
Decision:
Interpretation:
2
3. Consider the following scores in an experiment involving three conditions;
A
B
C
2
2
2
2
5
5
5
5
8
8
8
8
Without actually computing the sum of squares within, what must its value be?
Why? (12 points)
4. Insert the missing entries in the summary table for a one-way analysis of variance having three
levels of the independent variable and n = 25. (Each answer is 3 points)
Source
SS
df
MS
F
Between
___
___
___
___
Within
121
___
___
Total
141
3
Problem Set 5
1. A professor is wondering whether allowing students to use their notes during tests
improves performance. She uses one of her classes as a control group and does not
allow them to use their notes, and she allows her second class to use their notes while
taking their exams. Below are the grades for each 12 person class. Is there a difference
in grades due to being allowed to use notes?
Control Class
78
72
76
74
60
90
55
72
87
86
73
62
Open Notes Class
90
88
87
85
65
65
97
92
87
73
86
85
Research Problem (2 points):
Do students that have an access to their notes during tests improve their exam
scores?
Statistical Hypotheses (4 points):
Null Hypothesis: Having an access to notes during exam will not affect the exam
scores
µ1 = µ 2
Alternative Hypothesis: Having an access to notes during exam will significantly
affect the exam scores
µ1 ≠ µ2
Decision Rule (4 points):
Reject the null hypothesis at the .05 level of significance if t is greater than or equal to
2.074 or less than or equal to -2.074, given 22 degrees of freedom.
Calculations (copy and paste your Jamovi output here or upload a separate file with
your outputs to Blackboard.) (5 points)
Decision (5 points):
t = -2.23
Since t < -2.074, Reject the null hypothesis Interpretation (5 points): There is enough evidence to support the claim that having an access to notes during an exam will significantly affect the exam scores. 2. A developmental psychologist is interested in whether there is a difference in anxiety between parents and their children. A study is done involving one parent and the oldest child for each of 15 families, measuring the anxiety in each member of the pair. The data are below with higher scores indicating more anxiety. Do parents and their children differ? Family 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Parent 8 4 5 6 3 2 6 7 7 7 8 9 5 4 4 Child 6 5 5 5 8 6 7 7 8 9 8 6 3 2 3 Research Problem (2 points): Is there a difference in anxiety between parents and their children? Statistical Hypotheses (4 points): Null Hypothesis: There is no difference in the anxiety between parents and their children µ1 = µ 2 Alternative Hypothesis: There is a significant difference in the anxiety between parents and their children µ1 ≠ µ2 Decision Rule (4 points): Reject the null hypothesis at the .05 level of significance if t is greater than or equal to 2.145 or less than or equal to -2.145, given 14 degrees of freedom. Calculations (copy and paste your Jamovi output here or upload a separate file with your outputs to Blackboard.) (5 points) Decision (5 points): t = -0.345 Since t > -2.145, Fail to reject the null hypothesis
Interpretation (5 points):
There is not enough evidence to support the claim that there is a significant
difference in the anxiety between parents and their children.
3. A researcher hypothesizes that there has been an increase in felony prison sentences
over the past 5 years. In 2013 the average prison sentence was 9 years. The researcher
selects a random sample of prisoners currently serving prison terms for felonies and
finds that they have the following prison sentences. Has the average amount of time
that people are sentenced for felony convictions changed in the last 5 years?
Prison Sentences in Years
11, 13, 14, 15, 8, 9, 10, 11, 11, 10, 11, 12, 13, 14, 15, 7, 8
Research Problem (2 points):
Has the average amount of time that people are sentenced for felony
convictions changed in the last 5 years?
Statistical Hypotheses (4 points):
Null Hypothesis: The average amount of time that people are sentenced for
felony convictions has not changed in the last five years.
µ=9
Alternative Hypothesis: The average amount of time that people are sentenced
for felony convictions has changed in the last five years.
µ1 ≠ 9
Decision Rule (4 points):
Reject the null hypothesis at the .05 level of significance if t is greater than or equal
to 2.120 or less than or equal to -2.120, given 16 degree of freedom.
Calculations (copy and paste your Jamovi output here or upload a separate file with
your outputs to Blackboard.) (5 points)
Decision (5 points):
t = 3.83
Since t > 2.120, Reject Null Hypothesis
Interpretation (5 points):
There is enough evidence to support the claim that the average amount of
time that people are sentenced for felony convictions has changed in the last
five years
4. Researchers have a hypothesis that older siblings tend to be more extroverted than
their younger siblings. They collected data between 14 pairs of same sex siblings, and
found the following extraversion scores. Is there a difference between how extraverted
older and younger siblings are? (Extraversion is measured on a 50 point scale with
higher scores indicating more extraversion.)
Sibling
Pair
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Older
Sibling
48
42
36
29
45
22
25
35
45
50
36
24
33
39
Younger
Sibling
40
32
25
19
36
14
15
24
37
44
29
15
34
31
Question 4
Research Problem (2 points):
Is there a difference between how extraverted older and younger siblings are?
Statistical Hypotheses (4 points):
Null Hypothesis: There is no difference in the extraversion between older and
younger siblings
µ1 = µ 2
Alternative Hypothesis: There is a significant difference in the extraversion
between older and younger siblings
µ1 ≠ µ2
Decision Rule (4 points):
Reject the null hypothesis at the .05 level of significance if t is greater than or equal to
2.160 or less than or equal to -2.160, given 13 degree of freedom.
Calculations (copy and paste your Jamovi output here or upload a separate file with
your outputs to Blackboard.) (5 points)
Decision (5 points):
t = 10.1
Since t > 2.160, Reject Null Hypothesis
Interpretation (5 points):
There is enough evidence to support the claim that there is a significant
difference in the extraversion between older and younger siblings