Exercise Solution 14.1

We are given q = 0.9, α + 1 = 375 and ε = .05. Assuming null hypothesis script h naught 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]
  • [ab – 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].

 

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