33.

a. Apply the Wald procedure to derive a stopping rule for normal data with known s  15. Let H0:

m100, Ha: m110, a.05, b.05. Express the continuance of sampling in terms of the sum of the rst n observations. This should show that sampling continues as long as the sum is between two linear functions of n.

b. Apply your procedure to the following data

(see Example 1.2), IQ scores from a class of 33 students:

118 108 110 136 106 102 132 115 111 113 113 140 82 118 110 109 96 99 113 115 127 107 119 108 122 103 122 108 103 146 113 121 108

(Hint: The sums can be obtained from software, for example, the partial sums function in MINITAB.) What is your conclusion and how many observations are required?

c. Find the expected number of observations required under H0 and under Ha. In terms of the speci cations for this problem, what causes these two numbers to be the same?

d. Find the number required for a xed sample to achieve the same a and

b, and compare with the answer to part (c).