Members of the general adult population volunteer an average of 4.2 hours per we
ID: 3157166 • Letter: M
Question
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. 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? Females Males Sample size 20 18 Sample mean 3.8 2.5 Sample variance 3.5 2.2 A.No, because the test value 2.38 is greater than the critical value B.No, because the test value 2.38 does not exceed the critical value C.No, because the test value 2.90 is greater than the critical value D.Yes, because the test value 2.90 is greater than the critical value Reset Selection
Explanation / Answer
For independnet groups and small sample size, compute 2-sample t test.
SE(x1bar-x2bar)=sqrt[s1^2/n1+s2^2/n2], where x1bar and x2bar represent sample mean volunteer hour per week for female and male, s1^2 and s2^2 are sample variance, n1 and n2 are respective sample sizes.
=sqrt [3.5/20+2.2/18]
=0.545
t35,0.01=2.4377
t(obtained)=(x1bar-x2bar)/SE(x1bar-x2bar)
=(3.8-2.5)/0.545
=2.38
Option B) The test statistic do not fall in critical region.