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 (s = 1.72) for the 51 non-vegetarian students and 2.22 (s = 0.67) 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.

Difference = mu(1) - mu(2)
95% CI for difference: (-0.209716,2.129716)
T-Test of difference = 0(vs not =):
T-Value = 1.64 P-Value = 0.106 DF = 58
Both use Pooled StDev = 1.6162
95% CI for difference: (0.289196, 1.630804)
T-Test of difference = 0(vs not =):
T-Value = 2.92P@Value = 0.007DF = 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.

Transcribed Image Text:

Sample Mean StDev SEMe an 3.18 1 2.22 0.24 0.22 51 1.72 0.67 2