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].