Question

17.35 Hand Size. A clever way to determine hand size in three dimensions is to measure the volume in ml of water displaced when the hand is dipped in a water container. A study used this method to gather hand volumes of 12 male college students. Here are the measurements:

400, 360, 420, 520, 460, 350, 500, 420, 450, 430, 395, 400

We consider this an SRS of all male college students. Obtain a 95% confidence interval for the mean hand size and interpret it in context.

Answer 1

We have for given data,              
                  
Sample mean =425.42          
Sample standard deviation =50.966      
Sample size =12          
Level of significance=1-0.95=0.05          
Degree of freedom =11          
                  
t critical value is (by using t table)=   2.201          
                  
Confidence interval formula is                   


=(393.04 , 457.80)              
                  
                  
Lower confidence limit=393.04      
                  
Upper confidence limit=457.80      

We are 95% confident that population mean hand size is between 393.04 to 457.80