Question

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?

Answer 1

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