:4. Solution. 

 	
 SE of sum of 1971 sample scores = 14 x 40 = 560 

 	
 SE of average of 1971 sample scores = (560/1600) x 100% 

 	
       = 14/40 = 7/20 = 35/100 

 	
       = .35 

 	
 SE of sum of 1975 sample scores = same as 1971's = .35 

(The box SD is bootstraped by the sample SD in both cases)

 	
 
 	
 SE of the difference = the square root of (.35)^2 + (.35)^2 

 	
                      = .49 

 	
 z = ( 1975 ave - 1971 ave - 0 )/ SE of difference 

 	
   = (68.5 - 67.2)/.49 = 1.2/.49 = 2.6 

The area under the normal curve from -2.6 to 2.6 is 99.07%, so
the area to the right of 2.6 is .93/2 = .465%.

 	
 .465/100 = 4.65/1000 

 	
          = 5/1000 (approx) 

 	
          = 1/200