Answer
Data Set 1:
Lower Bound = 82.56
Upper Bound = 115.63
Data Set 2:
Lower Bound = 91.7
Upper Bound = 106.5
Data Set 3:
Lower Bound = 93.5
Upper Bound = 104.56
Work Step by Step
Data Set 1: Here we have n = 8, df = n-1 = 7, x̅ = 99.1 and s = 19.77
Confidence = 95%
α = 1 - 0.95 = 0.05, α/2 = 0.025, tα/2=2.365
$E=2.365 \times \frac{19.77}{\sqrt 8} = 16.53$
Lower Bound = x̅ - E = 99.1 - 16.53 = 82.56
Upper Bound = x̅ + E = 99.1 + 16.53 = 115.63
Data Set 2: Here we have n = 20, df = n-1 = 19, x̅ = 99.1 and s = 15.78
Confidence = 95%
α = 1 - 0.95 = 0.05, α/2 = 0.025, tα/2=2.093
$E=2.093 \times \frac{15.78}{\sqrt 20} = 7.385$
Lower Bound = x̅ - E = 99.1 - 7.385 = 91.7
Upper Bound = x̅ + E = 99.1 + 7.385 = 106.5
Data Set 3: Here we have n = 30, df = n-1 = 29, x̅ = 99.03 and s = 14.81
Confidence = 95%
α = 1 - 0.95 = 0.05, α/2 = 0.025, tα/2=2.045
$E=2.045 \times \frac{14.81}{\sqrt 30} = 5.53$
Lower Bound = x̅ - E = 99.03 - 5.53 = 93.5
Upper Bound = x̅ + E = 99.03 + 5.53 = 104.56
