In: Statistics and Probability
Construct the confidence interval for the population mean μ, if c = .95, | ||||
x-bar = 11.000, s = .4, and n = 100. |
Solution :
Given that,
= 11.000
s =0.4
n =100
Degrees of freedom = df = n - 1 = 100- 1 = 99
At 95% confidence level the t is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2= 0.05 / 2 = 0.025
t /2,df = t0.025,99 = 1.984 ( using student t table)
Margin of error = E = t/2,df * (s /n)
=1.984 * (0.4 / 100)
=0.0794
The 95% confidence interval estimate of the population mean is,
- E < < + E
11.000 - 0.0794 < <11.000+ 0.0794
10.9206< < 11.0794
( 10.9206, 11.0794 )