Answer:
(8.213 ; 8.247)
Step-by-step explanation:
Given the data :
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Dia. 8.23 8.16 8.23 8.25 8.26 8.23 8.20 8.26 8.19 8.23 8.20 8.28 8.24 8.25 8.24
Sanple size, n = 15
Sample mean, xbar = Σx / n = 123.45 / 15 = 8.23
The sample standard deviation, s = √(x -xbar)²/n-1
Using calculator :
Sample standard deviation, s = 0.03116
s = 0.031 (3 decimal places)
The 95% confidence interval :
C.I = xbar ± (Tcritical * s/√n)
Tcritical at 95%, df = 15 - 1 = 14
Tcritical = 2.145
C.I = 8.23 ± (2.145 * 0.031/√15)
C.I = 8.23 ± 0.0171689
C.I = (8.213 ; 8.247)