Let us say the life of a tire in miles, say X, is normally distributed with mean θ and standard deviation 5000. Past experience indicates that θ = 30,000. The manufacturer claims that the tires made by a new process have mean θ > 30,000. It is possible that θ = 35,000. Check his claim by testing H₀ : θ = 30,000 against H₁ : θ > 30,000. We observe n independent values of X, say x₁, . . . , x_n, and we reject H₀ (thus accept H₁) if and only if ¯x ≥ c. Determine n and c so that the power function _ϒ(θ) of the test has the values _ϒ(30,000) = 0.01 and _ϒ(35,000) = 0.98.