Question

Construct a confidence interval for μ based on the sample data given here:

12.3       11.6      11.9      12.8     11.5

11.4       12         11.7      11.8     11.5

Use 83% as the confidence level.

Round the final values to two digits after the decimal point.

The lower limit in the interval is:  and the upper limit in the interval is:  

Answer 1

We have for given data,                  
                  
Sample mean =11.85          
Sample standard deviation =0.4301      
Sample size =10          
Level of significance=1-0.83=0.17          
Degree of freedom =9          
                  
t critical value is (by using t table)=   1.492          
$\bar{x}\pm t*\frac{S}{\sqrt{n}}= 11.85 \pm 1.492 *(\frac { 0.4301 } {\sqrt{ 10 }})=( 11.6471 , 12.0529 )$

Lower confidence limit=11.65
      
Upper confidence limit=12.05