Answer
We are 99% confident that the mean depth of visibility of the Secchi disk is between 44.0 and 71.6 inches.
Work Step by Step
Here we have n = 12, df = n-1 = 11, x̅ = 57.8 and s = 15.4
Confidence = 99%
α = 1 - 0.99 = 0.01, α/2 = 0.005, $t_{α/2} = 3.106$
$E = 3.106 \times \frac{15.4}{\sqrt 12} = 13.8 $
Lower Bound = x̅ - E = 57.8 - 13.8 = 44
Upper Bound = x̅ + E = 57.8 + 13.8 = 71.6
Hence, we are 99% confident that the mean depth of visibility of the Secchi disk is between 44.0 and 71.6 inches.
