10.40 Vegetarians more liberal? When a sample of social science graduate students at the University of Florida gave their responses on political ideology (ranging from 1 = very liberal to 7 = very conservative ), the mean was 3.18 1s = 1.722 for the 51 nonvegetarian students and 2.22 1s = 0.672 for the 9 vegetarian students. Software for comparing the means provides the printout, which shows results first for inferences that assume equal population standard deviations and then for inferences that allow them to be unequal.

Sample N Mean StDev SE Mean 1 51 3.18 1.72 0.24 2 9 2.220 0.670 0.22 Difference = μ(1) − μ(2)
Estimate for difference: 0.960 95% CI for difference: (−0.210, 2.130)
T-Test of difference = 0(vs •): T-Value = 1.64 P-Value = 0.106 DF = 58 Both use Pooled StDev = 1.6162 95% CI for difference: (0.289, 1.631)
T-Test of difference = 0(vs •):
T-Value = 2.92 P-Value = 0.007 DF = 30

a. Explain why the results of the two approaches differ so much. Which do you think is more reliable?

b. State your conclusion about whether the true means are plausibly equal.