Answers for Testing for Statistical Significance Assignment

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Question 1: The university administration believes that there is a significant difference in
the reasons why people drink between males and females. In one sentence, identify if there is a
significant difference between males and females (be sure to provide the appropriate statistics
and p-values). What percentage of males say they drink alcohol because it’s the only way to
have a good time? What percentage of females drink because they enjoy the taste?
Crosstabs
Case Processing Summary
Cases
Mis sing
N
Percent
Valid
N
Percent
Why do you
drink? * Gender
135
83.3%
27
16.7%
Total
N
Percent
162
100.0%
Why do you drink? * Gender Crosstabulation
Why do
you
drink?
Enjoy the taste
Relaxes me
Becaus e my friends drink
Best way to have a good
time
Total
Count
% within Gender
Count
% within Gender
Count
% within Gender
Count
% within Gender
Count
% within Gender
Gender
Male
Female
22
14
29.3%
23.3%
36
40
48.0%
66.7%
3
1
4.0%
1.7%
14
5
18.7%
8.3%
75
60
100.0%
100.0%
Total
36
26.7%
76
56.3%
4
3.0%
19
14.1%
135
100.0%
Chi-Square Te sts
Pearson Chi-Square
Lik elihood Ratio
Linear-by-Linear
As soc iation
N of Valid Cases
Value
5.655a
5.819
1.115
3
3
As ymp. Sig.
(2-sided)
.130
.121
1
.291
df
135
a. 2 c ells (25.0%) have ex pec ted c ount les s than 5. The
minimum expected count is 1.78.
There is not a significant difference in the reasons why people drink between males
and females (X2 = 5.655, p ≤ .130).
18.7% of males say they drink alcohol to have a good time.
23.3% of females say they drink because they enjoy the taste
Question 2:
Melody, the bartender at the local watering hole, believed that student
preferences differed for shots depending on how they classified themselves in terms of drinking
(non-drinker, social drinker, moderate drinker, heavy drinker). In one sentence, identify if there is
a significant difference in the preference for shots by drinking self classification (be sure to
provide the appropriate statistics and p-values). If there are any significant differences, what are
they? Who likes shots the most?
Oneway
Descriptives
Preference for Shots
N
Nondrinker
Social drinker
Moderate drinker
Heavy drinker
Total
13
72
42
9
136
Mean
2.85
2.85
3.31
5.22
3.15
Std. Deviation
2.193
1.717
1.841
1.856
1.888
Std. Error
.608
.202
.284
.619
.162
95% Confidence Interval for
Mean
Lower Bound Upper Bound
1.52
4.17
2.44
3.25
2.74
3.88
3.80
6.65
2.83
3.47
Minimum
1
1
1
1
1
Maximum
7
7
7
7
7
ANOVA
Preference for Shot s
Between Groups
W ithin Groups
Total
Sum of
Squares
47.515
433.543
481.059
df
3
132
135
Mean Square
15.838
3.284
F
4.822
Sig.
.003
Post Hoc Tests
Multiple Com pari sons
Dependent Variable: Preference for Shots
Bonferroni
(I) Drinking
self-classification
Nondrinker
Social drinker
Moderate drink er
Heavy drinker
(J) Drinking
self-classification
Social drinker
Moderate drink er
Heavy drinker
Nondrinker
Moderate drink er
Heavy drinker
Nondrinker
Social drinker
Heavy drinker
Nondrinker
Social drinker
Moderate drink er
Mean
Difference
(I-J)
St d.
-.001
-.463
-2. 376*
.001
-.462
-2. 375*
.463
.462
-1. 913*
2.376*
2.375*
1.913*
E rror
.546
.575
.786
.546
.352
.641
.575
.352
.666
.786
.641
.666
Sig.
1.000
1.000
.018
1.000
1.000
.002
1.000
1.000
.028
.018
.002
.028
95% Confidenc e Interval
Lower Bound Upper Bound
-1. 46
1.46
-2. 00
1.08
-4. 48
-.27
-1. 46
1.46
-1. 40
.48
-4. 09
-.66
-1. 08
2.00
-.48
1.40
-3. 70
-.13
.27
4.48
.66
4.09
.13
3.70
*. The mean differenc e is significant at the .05 level.
There is a significant difference in preference for shots by drinking self classification (F =
4.822, p ≤ .003). There are significant differences between heavy drinkers (mean
preference = 5.22) and nondrinkers (mean = 2.85), social drinkers (mean = 2.85) and
moderate drinkers (mean = 3.31). Heavy drinkers like shots the most.
Question 3: The President of the University believes that, based on conversation with the
head of the police department, WEU students drink far more than the national average. In one
sentence, identify whether or not WEU students differ from the national average (be sure to
provide the appropriate statistics and p-values). How many drinks, on average, do WEU students
drink in a typical week?
T-Test
One-Sam ple Statistics
N
On average, how
many drink s do you
consume each week?
Mean
136
4.53
St d. Deviation
St d. Error
Mean
2.976
.255
One-Sample Test
Test Value = 2.5
t
On average, how
many drink s do you
consume each week?
7.952
df
135
Sig. (2-tailed)
Mean
Difference
.000
2.029
95% Confidenc e
Int erval of t he
Difference
Lower
Upper
1.52
WEU students differ from the national average in the number of drinks they consume each
week (t = 7.952, p ≤ .000). On average, WEU students drink 4.53 drinks per week.
2.53
Question 4: One of the brothers in Pi Mu Beta, a fraternity on campus said that women and
men at WEU differ in their preference of lite beer. In one sentence, identify whether or not there
is a difference between men and women in their preference for lite beer (be sure to provide the
appropriate statistics and p-values). Who prefers lite beer more, men or women? Is the result
what you expected? Why or why not?
T-Test
Group Statistics
Preference for Lite Beer
Gender
Male
Female
N
Mean
5.03
4.03
75
60
Std. Deviation
1.952
2.393
Std. Error
Mean
.225
.309
Independent Samples Test
Levene's Test for
Equality of Variances
F
Preference for Lite Beer
Equal variances
as sumed
Equal variances
not ass umed
7.245
Sig.
.008
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
2.656
133
.009
.993
.374
.254
1.733
2.597
112.991
.011
.993
.382
.236
1.751
There is a difference in preference for lite beer between men and women (t = 2.597, p ≤
.011). Males prefer lite beer more than females.
This isn’t what I expected. I though women might prefer liter beer more than men because
of it contains fewer calories.
Question 5: The university administration believes that there is a significant difference
between those who do and do not belong to a fraternity or sorority as to whether or not they drink
alcohol. In one sentence, identify whether or not there is a difference between Greeks and nonGreeks (be sure to provide the appropriate statistics and p-values). What percentage of those
who drink alcohol do not belong to a Greek organization?
Crosstabs
Ca se Processi ng Sum mary
N
Do you drink
alc ohol? * Belong t o
fraternity or sorority ?
Cases
Missing
N
Percent
Valid
Percent
161
99.4%
1
Total
Percent
N
.6%
162
100.0%
Do you drink alcohol? * Belong to fraternity or sorority? Crosstabulation
Do you drink
alcohol?
Yes
No
Total
Belong to fraternity or
sorority?
Yes
No
49
86
Count
% within Do you
drink alcohol?
% within Belong to
fraternity or sorority?
Count
% within Do you
drink alcohol?
% within Belong to
fraternity or sorority?
Count
% within Do you
drink alcohol?
% within Belong to
fraternity or sorority?
Total
135
36.3%
63.7%
100.0%
98.0%
77.5%
83.9%
1
25
26
3.8%
96.2%
100.0%
2.0%
22.5%
16.1%
50
111
161
31.1%
68.9%
100.0%
100.0%
100.0%
100.0%
Chi-Square Tests
Pearson Chi-Square
Continuity Correction a
Likelihood Ratio
Fis her's Exact Test
Linear-by-Linear
As sociation
N of Valid Cases
Value
10.722 b
9.260
14.139
10.655
df
1
1
1
1
As ymp. Sig.
(2-sided)
.001
.002
.000
Exact Sig.
(2-sided)
Exact Sig.
(1-sided)
.000
.000
.001
161
a. Computed only for a 2x2 table
b. 0 cells (.0%) have expected count less than 5. The minimum expected count is 8.
07.
There is a significant difference in whether or not a person consumes alcohol by whether
or not the student belongs to a fraternity or sorority (X2 = 10.722, p ≤ .000).
63.7% of those who do drink so not belong to a fraternity or sorority.
Question 6: Past research showed that college students, on average, rated wine coolers a
5.2 on a 1 to 7 scale where a “1” is I do not like and a “7” is I like very much. Dr. Jekyll thinks that
WEU students differed from the national average in terms of their preference for wine coolers
(wcooler). In one sentence, identify whether or not WEU students differ from the average college
students in terms of their preference for wine coolers (be sure to provide the appropriate statistics
and p-values).
T-Test
One-Sample Statistics
N
Preference for
Wine Cooler
Mean
136
3.55
Std. Deviation
Std. Error
Mean
2.135
.183
One-Sample Test
Test Value = 5.2
t
Preference for
Wine Cooler
-9.003
df
135
Sig. (2-tailed)
Mean
Difference
.000
-1.649
95% Confidence
Interval of the
Difference
Lower
Upper
-2.01
-1.29
WEU students differed from the average college student in terms of their preference for
wine coolers (t = -9.003, p ≤ .000).
Question 7: The Director of Greek Life (and former party animal) believes that people who
belong to a fraternity or sorority go out on average more nights per week than their non-Greek
classmates. In one sentence, identify if there is a difference in the number of nights a student
goes out on average between Greeks and non-Greeks (be sure to provide the appropriate
statistics and p-values).
T-Test
Group Sta tisti cs
Belong to fraternity
or sorority?
Yes
N
On average, how
many nights do you
go out eac h week? No
Mean
St d. Deviat ion
St d. Error
Mean
49
1.96
1.020
.146
86
1.49
.991
.107
Independent Samples Test
Levene's Test for
Equality of Variances
F
On average, how
many nights do you
go out each week?
Equal variances
as sumed
Equal variances
not ass umed
.517
Sig.
.473
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
2.626
133
.010
.471
.179
.116
.825
2.606
97.600
.011
.471
.181
.112
.829
There is a significant difference in the number of nights a student goes out per week
between Greeks and non-Greeks (t = 2.626, p ≤ .010).
Question 8: Students were asked their level of agreement or disagreement with the
statements I am a party animal and I am religious. The chair of the Religion Department
believes that students who state they are religious would not also say they are party animals. In
one sentence, identify if the chair’s position is indeed true (be sure to provide the appropriate
statistics and p-values).
T-Test
Paired Samples Statistics
Pair
1
Mean
2.10
3.69
I am a party animal
I am religious
N
Std. Deviation
.900
1.054
162
162
Std. Error
Mean
.071
.083
Paired Samples Correlations
N
Pair
1
I am a party animal
& I am religious
Correlation
162
.131
Sig.
.096
Paired Samples Test
Paired Differences
Mean
Pair
1
I am a party animal
- I am religious
-1.586
Std. Deviation
Std. Error
Mean
1.293
.102
95% Confidence
Interval of the
Difference
Lower
Upper
-1.787
-1.386
t
-15.613
df
Sig. (2-tailed)
161
The chair’s assertion would be true as there is a significant difference in a student’s level
of agreement/disagreement with “I am a party animal” and “I am religious” (t = -15.613, p ≤
.000).
.000
Question 9: The average WEU takes 14 credit hours per semester.
The advising
coordinator, Ms. Schedule, believes that there is a difference in the number of credit hours taken
by an individual’s work status. In one sentence, identify whether or not this difference exists (be
sure to provide the appropriate statistics and p-values). If there are any significant differences,
what are they?
Oneway
De scri ptives
Number of credit hours enrolled this semester
N
Do not work
W ork less than 20
hours per week
W orks 20 hours or
more per week
Total
95% Confidenc e Int erval for
Mean
Lower Bound Upper Bound
14.07
15.66
37
Mean
14.86
St d. Deviat ion
2.371
St d. Error
.390
Minimum
9
Maximum
19
94
15.20
2.367
.244
14.72
15.69
3
20
30
13.37
1.938
.354
12.64
14.09
9
17
161
14.78
2.384
.188
14.41
15.15
3
20
ANOVA
Number of credit hours enrolled this semester
Between Groups
W ithin Groups
Total
Sum of
Squares
76.941
832.451
909.391
df
2
158
160
Mean Square
38.470
5.269
F
7.302
Sig.
.001
Post Hoc Tests
Multiple Compari sons
Dependent Variable: Number of credit hours enrolled this semester
Bonferroni
(I) Work classification hours work ed each week
Do not work
W ork less than 20 hours
per week
W orks 20 hours or more
per week
(J) Work classificat ion hours work ed each week
W ork less than 20 hours
per week
W orks 20 hours or more
per week
Do not work
W orks 20 hours or more
per week
Do not work
W ork less than 20 hours
per week
Mean
Difference
(I-J)
St d. E rror
Sig.
95% Confidenc e Int erval
Lower Bound Upper Bound
-.337
.445
1.000
-1. 42
.74
1.498*
.564
.026
.13
2.86
.337
.445
1.000
-.74
1.42
1.835*
.481
.001
.67
3.00
-1. 498*
.564
.026
-2. 86
-.13
-1. 835*
.481
.001
-3. 00
-.67
*. The mean differenc e is significant at the .05 level.
There is a significant difference in the number of credits students take each semester by
work status (F = 7.302, p ≤ .001).
There were significant differences between those who worked 20 hours or more each week
(mean credit hours taken = 13.37) and students who did not work (mean credit hours =
14.86) and students who work less than 20 hours each week (mean credit hours = 15.20).
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