Exercise Solution 14.1

We are given q = 0.9, α + 1 = 375 and ε = .05. Assuming null hypothesis that q* = q = 0.9, X ~ B(375, 0.1). We use this to determine a = 27 and b = 49, and consider the three possible non-rejection intervals.

• [a, b] = [27,  49]
• [a + 1, b] = [28,  49]
• [a, b – 1] = [27,  48]

We calculate probabilities:

• Pr(X ∉ [27,  49]) = 0.047
• Pr(X ∉ [28,  49]) = 0.061
• Pr(X ∉ [27,  48]) = 0.058

The second and third probabilities exceed 0.05, so our non-rejection interval is [27,  49].