Do college students who have volunteered for community service work differ from those who have not? A study obtained data from 57 students who had done service work and 18 who had not.
Group |
Condition |
N |
X bar |
S |
1 |
Service |
57 |
104.12 |
14.60 |
2 |
No Service |
18 |
97.82 |
14.20 |
Is there strong evidence (a=0.05 significance level) that students who have engaged in community service are on the average more attached to their friends. Please show all working.
1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested.
This corresponds to a right-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.
2) Rejection Region
Based on the information provided, the significance level is a=0.05, and the degrees of freedom are df = 73. In fact, the degrees of freedom are computed as follows, assuming that the population variance are eual:
Hence, it is found that the critical value for this right-tailed test is t_{c} = 1.666,
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