# 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].