Answer
Data Set 1:
Lower Bound = 58.6
Upper Bound = 117.16
Data Set 2:
Lower Bound = 83.25
Upper Bound = 105.95
Data Set 3:
Lower Bound = 88.1
Upper Bound = 103.9
Work Step by Step
Data Set 1: Here we have n = 8, df = n-1 = 7, x̅ = 87.88 and s = 35.02
Confidence = 95%
α = 1 - 0.95 = 0.05, α/2 = 0.025, tα/2=2.365
$E=2.365 \times \frac{35.02}{\sqrt 8} = 29.28$
Lower Bound = x̅ - E = 87.88 - 29.28 = 58.6
Upper Bound = x̅ + E = 87.88 + 29.28 = 117.16
Data Set 2: Here we have n = 20, df = n-1 = 19, x̅ = 94.6 and s = 24.26
Confidence = 95%
α = 1 - 0.95 = 0.05, α/2 = 0.025, tα/2=2.093
$E=2.093 \times \frac{24.26}{\sqrt 20} = 11.35$
Lower Bound = x̅ - E = 94.6 - 11.35 = 83.25
Upper Bound = x̅ + E = 94.6 + 11.35 = 105.95
Data Set 3: Here we have n = 30, df = n-1 = 29, x̅ = 96 and s = 21.1
Confidence = 95%
α = 1 - 0.95 = 0.05, α/2 = 0.025, tα/2=2.045
$E=2.045 \times \frac{21.12}{\sqrt 30} = 7.885$
Lower Bound = x̅ - E = 96 - 7.885 = 88.1
Upper Bound = x̅ + E = 96 + 7.885 = 103.9
