For random sample of Harvard University psychology majors, the responses on political ideology had a mean of 3.18 and the standard deviation of 1.72 for 51 non-vegetarian students and the mean of 2.22 and a standard deviation of 0.67 for the 20 vegetarian students. Defining appropriate notation, State the null and alternative hypothesis for testing whether there is a difference between population mean ideology for vegetarian and none of vegetarian soup.