A population is estimated to have a standard deviation of 10

A population is estimated to have a standard deviation of 10. We want to estimate the population mean within 2, with a 98 percent level of confidence. How large a sample is required?

Solution

98% confidence means z value = 2.33

Margin of error = 2

Hence 2.33(std error) =2

or std error = 0.8584

Std dev = 10

i.e. 2.33(10/rtn) = 2

Or rtn = 23.3/2 = 11.65

n = 135.7 = 136