can someone help me solve this problem seafch go book conten

seafch go book contents Answer 14. SAT coaching: A sample of 32 students took a class designed to improve their SAT math scores. Following are their scores before and after the class. Before After 383 334 378 467 470 473 443 459 426 493 382 473 408 433 478 502 420 368 396 488 489 473 448 473 428 525 382 474 407 434 490 508 430 394

Solution

a)

              
Calculating the standard deviation of the differences ,
              
s =    13.56075784          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    2.397225957          
              
Calculating the mean of the differences (third column):              
              
XD =    12.90625          
      
              
For the   0.95   confidence level,      
              
alpha/2 = (1 - confidence level)/2 =    0.025          
t(alpha/2) =    2.039513446          
              
lower bound = [X1 - X2] - t(alpha/2) * sD =    8.017075427          
upper bound = [X1 - X2] + t(alpha/2) * sD =    17.79542457          
              
Thus, the confidence interval is              
              
(   8.017075427   ,   17.79542457   ) [ANSWER]

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b)

YES, IT CONTRADICTS IT. The confidence interval is totally less than 20 points. [CONCLUSION]