Among the standard personality inventories used by psychologists is the thematic apperception test (TAT) in which a subject is shown a series of pictures and is asked to make up a story about each one. Interpreted properly, the content of the stories can provide valuable insights into the subject€™s mental well-being. The following data show the TAT results for 40 women, 20 of whom were the mothers of normal children and 20 the mothers of schizophrenic children. In each case the subject was shown the same set of 10 pictures. The figures recorded were the numbers of stories (out of 10) that revealed a positive parent€“child relationship, one where the mother was clearly capable of interacting with her child in a flexible, open-minded way (199).

(a) Test H0: σ2X = σ2Y versus H1: σ2X ‰  σ2Y, where σ2X and σ2Y are the variances of the scores of mothers of normal children and scores of mothers of schizophrenic children, respectively. Let α = 0.05.
(b) If H0: σ2X = σ2Y is accepted in part (a), test H0: μX = μY versus H1: μX ‰  μY. Set α equal to 0.05.

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TAT Scores Mothers of Normal Children Mothers of Schizophrenic Children