Suppose that a sample of 81 people produces a 95% confidence interval of 195 < μ < 227 for a population mean. To one decimal place, what is the sample standard deviation?
Solution :
Sample mean =
= (195 + 227) / 2 = 211
Margin of error = E = Upper confidence interval -
= 227 - 211 = 16
t/2,df
= 1.990
Margin of error = E = t/2,df
* (s /
n)
s = E *
n / t
/2,df
= 16 *
9 / 1.99 = 24.1
sample standard deviation = 24.1
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