Question

Using the following information:

Sample mean 0.53, sample size of 6, and sample standard deviation 0.0559

Find a 95% confidence interval for the population mean.

Answer 1

solution

Given that,

= 0.53

s =0.0559

n = 6

Degrees of freedom = df = n - 1 = 6- 1 = 5

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,5 = 2.571 ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 2.571 * ( 0.0559/ 6) = 0.0587

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

- E < < + E

0.53 - 0.0587 < < 0.53+ 0.0587

0.4713< < 0.5887

( 0.4713, 0.5887 )