We are conducting a follow-up investigation. We aim to compare the mean time spent on social media between states (NY-NJ, NY-CT, NJ-CT). It is hypothesized that average time spent on social media between two states is statistically equal and tests whether this is the case. The result of the mean difference test is presented in Appendix 3.
Q5. Find the hypothesis test result from Appendix 3 regarding the mean difference test, then analyze the outcomes of the hypothesis test for each comparison (NY-NJ, NY-CT, NJ-CT). Subsequently, elaborate on the contributing factors toward your conclusion.
a) Conclusion for the hypothesis ($µ_{NY} = µ_{NJ}$)
b) Conclusion for the hypothesis ($µ_{NY} = µ_{NJ}$)
(Appendix 3)
1) NY and NJ
Mean
NY
NJ
60.93 64.2666667
Variance
215.50 191.780952
Observations
15
15
Pooled Variance
203.638095
Hypothesized Mean Difference
0
Df
28
t Stat
-0.6397
P(T<=t) one-tail
0.2638
t Critical one-tail
1.7011
P(T<=t) two-tail
0.5276
t Critical two-tail
2.0484
2) NY and CT
NY
CT
Mean
60.93
61.60
c) Conclusion for the hypothesis ($µ_{NY} = µ_{NJ}$)
Variance
215.50
200.11
Observations
15
15
Pooled Variance
207.804762
Hypothesized Mean Difference
0
Df
28
t Stat
-0.1267
P(T<=t) one-tail
0.4501
t Critical one-tail
1.7011
P(T<=t) two-tail
0.9001
t Critical two-tail
2.0484
3) NJ and CT
NJ
CT
Mean
64.27
61.60
Variance
191.78
200.11
Observations
15
15
Pooled Variance
195.947619
Hypothesized Mean Difference
0
Df
28
t Stat
0.5217
P(T<=t) one-tail
0.3030
t Critical one-tail
1.7011
P(T<=t) two-tail
0.6060
t Critical two-tail
2.0484