For a random sample of Harvard University psychology majors

For a random sample of Harvard University psychology majors, the responses on political ideology had a mean of 3.18 and a standard deviation of 1.72 for 51 nonvegetarian students and a mean of 2.22 and a standard deviation of 0.67 for 20 vegetarian students .

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

B. When we use software to compare the means with a significance test, we obtain the following 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.

Solution

(A) Let mu1 be the mean for vegetarian students

Let mu2 be the mean for nonvegetarian students

Null hypothesis: mu1=mu2

Alternative hypothesis: mu1 not equal to mu2

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(B) Assume that the significant level a=0.05

Since the p-value is 0.006 which is less than the significant level a=0.05, we reject the null hypothesis.