If n=26, ¯xx¯(x-bar)=31, and s=5, find the margin of error at a 99% confidence level
Solution :
Given that,
Point estimate = sample mean = = 31
sample standard deviation = s = 5
sample size = n = 26
Degrees of freedom = df = n - 1 = 26 - 1 = 25
At 99% confidence level
= 1 - 99%
=1 - 0.99 =0.01
/2
= 0.005
t/2,df
= t0.005,25 = 2.787
Margin of error = E = t/2,df * (s /n)
= 2.787 * ( 5 / 26)
Margin of error = E = 2.73
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