Let X1, X2, . . . , Xn be a random sample from a continuous probability distribution having median ~

(so that P(Xi  ~

)

P(Xi  ~

)
.5).

a. Show that P(min(Xi

)  ~

 max(Xi

))
1  

1 2



n1 so that (min(xi

), max(xi

)) is a 100(1  )% confidence interval for ~

with 


1 2



n1

. [Hint: The complement of the event {min(Xi

)  ~

 max(Xi

)} is {max(Xi

)  ~

}

{min(Xi

)  ~

}. But max(Xi

)  ~

iff Xi  ~

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. Nutrition, 1964:

322–330).

c. Let x(2) denote the second smallest of the xis and x(n1)

denote the second largest of the xis. What is the confidence coefficient of the interval (x(2), x(n1)) for ~

?