According to a theory in psychology, young female adults show more emotional empathy toward others than do males. The Journal of Moral Education (June 2010) tested this theory by examining the attitudes of a sample of 30 female college students. Each student completed the Ethic of Care Interview, which consisted of a series of statements on empathy attitudes. For the statement on emotional empathy (e.g., "I often have tender, concerned feelings for people less fortunate than me"), the sample mean response was 3.28. Assume the population standard deviation for females is .5. [Note: Empathy scores ranged from 0 to 4, where 0 = "never" and 4 = "always".] Suppose it is known that male college students have an average emotional empathy score of μ = 3.
a. Specify the null and alternative hypotheses for testing whether female college students score higher than 3.0 on the emotional empathy scale.
b. Compute the test statistic.
c. Find the observed significance level (p-value) of the test.
d. At α = .01, what is the appropriate conclusion?
e. How small of an α -value can you choose and still have sufficient evidence to reject the null hypothesis?