Solution:
x | x2 |
12.3 | 151.29 |
11.6 | 134.56 |
11.9 | 141.61 |
12.8 | 163.84 |
12.1 | 146.41 |
11.4 | 129.96 |
12 | 144 |
11.7 | 136.89 |
11.8 | 139.24 |
13.1 | 171.61 |
∑x=120.7 | ∑x2=1459.41 |
Mean ˉx=∑xn
=12.3+11.6+11.9+12.8+12.1+11.4+12+11.7+11.8+13.1/10
=120.7/10
=12.07
Sample Standard deviation S=√∑x2-(∑x)2nn-1
=√1459.41-(120.7)210/9
=√1459.41-1456.849/9
=√2.561/9
=√0.2846
=0.5334
Degrees of freedom = df = n - 1 = 10 - 1 =9
At 97% confidence level the t is ,
= 1 - 97% = 1 - 0.97 = 0.03
/ 2 = 0.03 / 2 = 0.015
t /2,df = t0.015,9=2.574
Margin of error = E = t/2,df * (s /n)
= 2.574 * (0.53 / 10)
= 0.43
Margin of error = 0.43
The 97% confidence interval estimate of the population mean is,
- E < < + E
12.07 - 0.43 < < 12.07 + 0.43
11.64 < < 12.50
(11.64, 12.50 )
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