Let be a random sample from a continuous probability distribution having median (so that

).

a. Show that so that (min(xi

), max(xi

)) is a confidence interval for with . [Hint: The complement of the event is

. But iff for all i.]

b. For each of six normal male infants, the amount of the amino acid alanine (mg/100 mL) was determined while the infants were on an isoleucine-free diet, resulting in the following data:

2.84 3.54 2.80 1.44 2.94 2.70 Compute a 97% CI for the true median amount of alanine for infants on such a diet (“The Essential Amino Acid Requirements of Infants,” Amer. J. of Nutrition, 1964: 322–330).

c. Let x(2) denote the second smallest of the xi

’s and denote the second largest of the xi

’s. What is the confidence level of the interval for ?