Members of the general adult population volunteer an average of 4.2 hours per week. A random sample of 20 female college students and 18 male college students produced the results given in the table below. Assuming that the variances of the time volunteered by females and males are equal, at the .01 level of significance, is there sufficient evidence to conclude that a difference exists between the mean number of volunteer hours per week for male and female college students?
Sample size 20 18
Sample mean 3.8 2.5
Sample variance 3.5 2.2
A. No, because the test value 2.36 is greater than the critical value
B. No, because the test value 2.36 does not exceed the critical value
C. No, because the test value 2.58 is greater than the critical value
D. Yes, because the test value 2.58 is greater than the critical value
The solution provides step by step method for the calculation of test statistic for independent sample t test. Formula for the calculation and Interpretations of the results are also included.