Question

A sample of 100 items has a population standard deviation of 5.1 and a mean of 21.6. Construct a 95 percent confidence interval for ?.

Answer 1

Solution :

Given that,

= 21.6

= 5.1

n = 100

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z_/2* ( /n)

=1.96 * (5.1 / 100)

= 0.9996

At 95% confidence interval estimate of the population mean is,

- E < < + E

21.6 - 0.9996 < < 21.6 +  0.9996

20.6004 < < 22.5996

(20.6004 , 22.5996 )