Answer:
(16.904 ; 30.660)
Step-by-step explanation:
Given the data :
X = 23.71,17.79,29.87,18.78,28.76
Sample size = 5
Mean = (23.71+17.79+29.87+18.78,+28.76) / 5 = 23.782
Using a calculator, sample standard deviation :
Standard deviation, s = 5.54
Tcritical at α = 0.05, df = 5 - 1 = 4
Using tables ; Tcritical value = 2.7763
Confidence interval :
Mean ± Margin of Error
Margin of Error (MOE) = Tcritical * SE
Margin of Error = Tcritical * s/sqrt (n)
MOE = 2.7763 * 5.54/Sqrt(5) = 6.878
Confidence interval : 23.782 ± 6.878
Lower boundary : 23.782 - 6.878 = 16.904
Upper boundary = 23.782 + 6.878 = 30.66
(16.904 ; 30.660)
