45. Cushing s disease is characterized by muscular weakness due to adrenal or pituitary dysfunction. To provide effective treatment, it is important to detect childhood Cushing s disease as early as possible.
Age at onset of symptoms and age at diagnosis for 15 children suffering from the disease were given in the article Treatment of Cushing s Disease in Childhood and Adolescence by Transphenoidal Microadenomectomy (New Engl. J. Med., 1984: 889).
Here are the values of the differences between age at onset of symptoms and age at diagnosis:
24 12 55 15 30 60 14 21 48 12 25 53 61 69 80

a. Does the accompanying normal probability plot cast strong doubt on the approximate normality of the population distribution of differences?

b. Calculate a lower 95% con dence bound for the population mean difference, and interpret the resulting bound.

c. Suppose the (age at diagnosis)  (age at onset)
differences had been calculated. What would be a 95% upper con dence bound for the corresponding population mean difference?