Antisocial personality disorder (ASPD) is characterized by deceitfulness, reckless disregard for the well-being of others, a diminished capacity for remorse, superficial charm, thrill seeking, and poor behavioral control. ASPD is not normally diagnosed in children or adolescents, but antisocial tendencies can sometimes be recognized in childhood or early adolescence. James Blair and his colleagues have studied the ability of children with antisocial tendencies to recognize facial expressions that depict sadness, happiness, anger, disgust, fear, and surprise. They have found that children with antisocial tendencies have selective impairments, with significantly more difficulty recognizing fearful and sad expressions. Suppose you have a sample of 25 16-year-old children with antisocial tendencies and you are particularly interested in the emotion of sadness. The average 16-year-old has a score on the emotion recognition scale of 12.50. (The higher the score on this scale, the more strongly an emotion has to be displayed to be correctly identified. Therefore, higher scores indicate greater difficulty recognizing the emotion). Assume that scores on the emotion recognition scale are normally distributed. You believe that children with antisocial tendencies will have a harder time recognizing the emotion of sadness (in other words, they will have higher scores on the emotion recognition test).

a. What is your null hypothesis stated using symbols?
b. What is your alternative hypothesis stated using symbols?
c. This is a tailed test. Given what you know, you will evaluate this hypothesis using a statistic.