1. For a random sample of Harvard University psychology majors, the responses on political ideology had a mean of 3.18 and standard deviation of 1.72 for 51 nonvegetarian students and a mean of 2.22 and standard deviation of .67 for the 20 vegetarian students.

a. Defining appropriate notation, state the null and alternative hypotheses for testing whether there is a difference between the population mean ideology for vegetarian and non-vegetarian students.

b. When we use software to compare the means with a significance test, we obtain the printout

Variances T DF Prob>|T|

------------- -------- -------- ----------

Unequal 2.9146 41.9 0.006

Interpret the P-value, in context, based on its definition. (Note: You are not being asked to make a decision at some -level.)