Answer
Lower Bound = 0.1677, Upper Bound = 0.1683. Since 1.68 is present in the 95% confidence interval, we fail to reject the null hypothesis. Thus there is not enough evidence to say that the golf balls do not conform to the 1.68 inch size standard.
Work Step by Step
$H_{o}$: μ = 1.68, $H_{a}: μ \ne 1.68$
Here we have: n = 12, x̅ = 1.681, s = 0.005, df = n-1 = 11 and Confidence = 95%
α = 1 - 0.95 = 0.05, α/2 = 0.025
Using Table-VI, we have:
$t_{0.025} = 2.201$
$E = 1.68 \times \frac{0.005}{\sqrt 12} = 0.003$
Lower Bound = x̅ - E = 1.68 - 0.003 = 0.1677
Upper Bound = x̅ + E = 1.68 + 0.003 = 0.1683
