Question

We draw a random sample of size 36 from a population with standard deviation 3.2. If the sample mean is 27, what is a 95% confidence interval for the population mean?

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 27

Population standard deviation =    = 3.2

Sample size n =36

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96 * ( 3.2 / 36 )

= 1.045
At 95% confidence interval estimate of the population mean
is,

- E < < + E

27 - 1.045 <   < 27 + 1.045

(25.955 , 28.045)