Question

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.

Answer 1

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,