Answer
Lower Bound = 47.516
Upper Bound = 52.984
The confidence interval has decreased because of the increased sample size.
Work Step by Step
Here we have n = 36, df = n-1 = 11, x̅ = 50.25 and s = 7.454
Confidence = 95%
α = 1 - 0.95 = 0.05, α/2 = 0.025, $t_{α/2} = 2.201$
$E = 2.201 \times \frac{7.454}{\sqrt 36} = 2.734 $
Lower Bound = x̅ - E = 50.25 - 2.734 = 47.516
Upper Bound = x̅ + E = 50.25 + 2.734 = 52.984
