Question

The following sample data are from a normal population: 10, 8, 11, 12, 9, 10, 14, 13,6 

a. What is the sample mean x̅? 

b. What is the sample standard deviation s? 

c. What is the 95% confidence interval for the population mean?

Answer 1

We have for given data,  

a)  
          
Sample mean =10.33........................using AVERAGE command in Excel.
b)  
Sample standard deviation =2.5..........................using STDEV in Excel.

c)
Sample size =   9  
Level of significance=   0.05  
Degree of freedom =   8  
          
t critical value is (by using t table)=   2.306  
          
Confidence interval formula is           
$\bar{x}\pm t*\frac{S}{\sqrt{n}}$
$=10.33\pm 2.306*\frac{2.5}{\sqrt{9}}$
=(8.41,12.25)  
          
          
Lower confidence limit=   8.41  
          
Upper confidence limit=   12.25