Students in an introductory statistics course were asked how many brothers and s
ID: 3042719 • Letter: S
Question
Students in an introductory statistics course were asked how many brothers and sisters they have and whether their hometown is urban or rural.
Number of Siblings in Rural versus Urban Areas
Rural
Urban
Rural
Urban
3
1
1
1
2
0
4
0
1
1
1
1
1
1
1
1
2
0
1
2
1
0
1
3
1
6
2
1
2
2
1
2
2
8
2
2
1
1
5
1
1
Use SPSS to test for a significant difference between rural and urban areas using the Wilcoxon rank-sum test. (4 points)
Use SPSS to test for a significant difference using the parametric two-sample independent t-test (4 points)
Compare the results of the two sample t-test and the Wilcoxon rank-sum test. Are the results different? Explain why or why not. (Bonus: 2 points)
Rural
Urban
Rural
Urban
3
1
1
1
2
0
4
0
1
1
1
1
1
1
1
1
2
0
1
2
1
0
1
3
1
6
2
1
2
2
1
2
2
8
2
2
1
1
5
1
1
Explanation / Answer
Answer:
Use SPSS to test for a significant difference between rural and urban areas using the Wilcoxon rank-sum test. (4 points)
Mann-Whitney Test
Ranks
Group
N
Mean Rank
Sum of Ranks
Number of Siblings
Rural
24
25.60
614.50
Urban
17
14.50
246.50
Total
41
Test Statisticsa
Number of Siblings
Mann-Whitney U
93.500
Wilcoxon W
246.500
Z
-3.171
Asymp. Sig. (2-tailed)
.002
a. Grouping Variable: Group
Calculated test value =93.5, P=0.002 which is < 0.05 level of significance. Ho is rejected.
We conclude that there is a significant difference between rural and urban areas.
Use SPSS to test for a significant difference using the parametric two-sample independent t-test (4 points)
Group Statistics
Group
N
Mean
Std. Deviation
Std. Error Mean
Number of Siblings
Rural
24
2.04
1.334
.272
Urban
17
1.24
1.821
.442
Independent Samples Test
Levene's Test for Equality of Variances
t-test for Equality of Means
F
Sig.
t
df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the Difference
Lower
Upper
Number of Siblings
Equal variances assumed
.001
.973
1.638
39
.109
.806
.492
-.189
1.802
Equal variances not assumed
1.554
27.699
.132
.806
.519
-.257
1.870
Calculated t test value =1.554, P=0.132 which is > 0.05 level of significance. Ho is not rejected.
We conclude that there is no significant difference in mean number of children between rural and urban areas.
Compare the results of the two sample t-test and the Wilcoxon rank-sum test. Are the results different? Explain why or why not. (Bonus: 2 points)
The results are different. This may be due to data not follows the assumptions of parametric t test. The data is not normally distributed. Nonparametric method may be appropriate here.
Ranks
Group
N
Mean Rank
Sum of Ranks
Number of Siblings
Rural
24
25.60
614.50
Urban
17
14.50
246.50
Total
41