The effect of loneliness among college students was examined in the article “The Importance of Perceived Duration: Loneliness and Its Relationship to Self- Esteem and Academic Performance” (Journal College Student Development [1994]: 456–460). Based on reported frequency and duration of loneliness, subjects were divided into two groups. The first group was the short-duration loneliness group, and the second was the long-duration loneliness group. A self-esteem inventory was administered to students in both groups. For the short-duration group, the reported mean self-esteem score was 76.78 and the standard deviation was 17.80. For the long-duration group, the mean and standard deviation were 64.00 and 15.68, respectively.

Do the data support the researcher’s claim that mean self-esteem is lower for students classified as having long-duration loneliness? Test the relevant hypotheses using α = .01. Be sure to state any assumptions that are necessary for your test to be valid.