Q2) Use the statistics calculated in “Q1” to conduct the following hypothesis te
ID: 3126386 • Letter: Q
Question
Q2) Use the statistics calculated in “Q1” to conduct the following hypothesis test.
The political science department of a public university is interested in determining if a person’s political affiliation affects their likelihood that they respect the government’s authority. To answer this question, they randomly polled separate groups of individuals with ‘Conservative’, ‘Moderate’, and ‘Liberal’ political views. For each subject within each group, the researchers asked questions and computed a “Cooperation with Police” score for each subject. “Cooperation with Police” serves as a measure for each person’s respect for government authority. Conduct an ANOVA (full hypothesis test) to determine if political view influences respect for government authority. If the ANOVA indicates that all population means are not equal determine which population mean is different using independent sample t-tests.
For this test, use a p-value of .05 to set your critical value and make sure to show all 5 steps of the hypothesis test. Show as much of your work as possible
New York City Based SampleExplanation / Answer
The political science department of a public university is interested in determining if a person’s political affiliation affects their likelihood that they respect the government’s authority. To answer this question, they randomly polled separate groups of individuals with ‘Conservative’, ‘Moderate’, and ‘Liberal’ political views. For each subject within each group, the researchers asked questions and computed a “Cooperation with Police” score for each subject. “Cooperation with Police” serves as a measure for each person’s respect for government authority. Conduct an ANOVA (full hypothesis test) to determine if political view influences respect for government authority. If the ANOVA indicates that all population means are not equal determine which population mean is different using independent sample t-tests.
For this test, use a p-value of .05 to set your critical value and make sure to show all 5 steps of the hypothesis test.
White
Hispanic
African American
count
6
6
6
mean
3.0000
2.8750
2.0833
sample standard deviation
0.6325
0.3446
0.3028
Total
sum
18.0000
17.2500
12.5000
47.7500
sum of squares
56.0000
50.1875
26.5000
132.6875
ANOVA table
Source
SS
df
MS
F
p-value
Treatment
2.9653
2
1.48264
7.29
.0062
Error
3.0521
15
0.20347
Total
6.0174
17
Table value of F(2,15) at 5% level=3.68
Calculated F=7.29 > 3.68 the table value
The null hypothesis is rejected.
Comparing White with Hispanic
Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.05
Population 1 Sample
Sample Size
6
Sample Mean
3
Sample Standard Deviation
0.6325
Population 2 Sample
Sample Size
6
Sample Mean
2.875
Sample Standard Deviation
0.3446
Intermediate Calculations
Population 1 Sample Degrees of Freedom
5
Population 2 Sample Degrees of Freedom
5
Total Degrees of Freedom
10
Pooled Variance
0.2594
Standard Error
0.2940
Difference in Sample Means
0.1250
t Test Statistic
0.4251
Two-Tail Test
Lower Critical Value
-2.2281
Upper Critical Value
2.2281
p-Value
0.6798
Do not reject the null hypothesis
Comparing White with African American
Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.05
Population 1 Sample
Sample Size
6
Sample Mean
3
Sample Standard Deviation
0.632455532
Population 2 Sample
Sample Size
6
Sample Mean
2.083333333
Sample Standard Deviation
0.302765035
Intermediate Calculations
Population 1 Sample Degrees of Freedom
5
Population 2 Sample Degrees of Freedom
5
Total Degrees of Freedom
10
Pooled Variance
0.2458
Standard Error
0.2863
Difference in Sample Means
0.9167
t Test Statistic
3.2022
Two-Tail Test
Lower Critical Value
-2.2281
Upper Critical Value
2.2281
p-Value
0.0095
Reject the null hypothesis
Comparing Hispanic with African American
Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.05
Population 1 Sample
Sample Size
6
Sample Mean
2.875
Sample Standard Deviation
0.344601219
Population 2 Sample
Sample Size
6
Sample Mean
2.083333333
Sample Standard Deviation
0.302765035
Intermediate Calculations
Population 1 Sample Degrees of Freedom
5
Population 2 Sample Degrees of Freedom
5
Total Degrees of Freedom
10
Pooled Variance
0.1052
Standard Error
0.1873
Difference in Sample Means
0.7917
t Test Statistic
4.2274
Two-Tail Test
Lower Critical Value
-2.2281
Upper Critical Value
2.2281
p-Value
0.0018
Reject the null hypothesis
White
Hispanic
African American
count
6
6
6
mean
3.0000
2.8750
2.0833
sample standard deviation
0.6325
0.3446
0.3028
Total
sum
18.0000
17.2500
12.5000
47.7500
sum of squares
56.0000
50.1875
26.5000
132.6875
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