 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2012/o/o5/f/solution

p > α

implies

1 - Φ (n (\overline{x} - μ_{0})) > α ⟺ n (\overline{x} - μ_{0}) < z_{α} .

Rearranging gives

μ_{0} > \overline{x} - \frac{z _{α}}{n}, so μ_{0} \in (\overline{x} - \frac{z _{α}}{n}, \infty) .

This is the confidence-interval/test duality for the matching one-sided procedures. The strict inequalities agree with the printed open interval.

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