Answer: 206 ± 8.069
Step-by-step explanation: Since the confidence interval is 95%, α = 0.025.
mean = 206
s = 12.7
standard error (SE) = [tex]\frac{12.7}{\sqrt{12} }[/tex]
SE = 3.66
The population is small, so use t-score. To do so, the degrees of freedom is:
n - 1 = 11
α = 0.025
Looking the t-score table for line 11 and column 0.025:
t-score = 2.201
Confidence interval will be:
mean ± t*SE
206 ± 2.201*3.66
206 ± 8.069
The confidence interval for the true mean is 206 ± 8.069
