Question

n a random sample of 38 criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was 70 ​months, with a standard deviation of 5 months. Construct and interpret a 95​% confidence interval for the mean length of sentencing for this crime.

Answer 1

We have given that,                  
                  
Sample mean =70   months      
Sample standard deviation =5 months      
Sample size =38          
Level of significance=1-0.95=0.05          
Degree of freedom =37          
                  
t critical value is (by using t table)=2.026          
                  
Confidence interval formula is                   


=(68.36,71.64)

We are 95% confident that population mean  length of sentencing for this crime is between 68.36 months to 71.64 months.