Question

Twenty five high school students complete a preparation program for taking the SAT test. Here are the SAT scores from the 25 students who completed the SAT prep program: 434 694 457 534 720 400 484 478 610 641 425 636 454 514 563 370 499 640 501 625 612 471 598 509 531 The mean of these scores is 536.00. We know that the population average for SAT scores is 500 with a standard deviation of 100. The question is, are these students’ SAT scores significantly greater than a population mean of 500 with a population standard deviation of 100 ? Note that the the maker of the SAT prep program claims that it will increase (and not decrease) your SAT score. So, you would be justified in conducting a one-directional test. (alpha = .05).

Choose between

A - The prep program didn't result in significant improvement in SAT scores

B- The prep program resulted in significant improvement in SAT scores

Answer 1

Ho :   µ =   500                  
Ha :   µ >   500       (Right tail test)          
                          
Level of Significance ,    α =    0.05                  
population std dev ,    σ =    100.0000                  
Sample Size ,   n =    25                  
Sample Mean,    x̅ =   536.0000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   100.0000   / √    25   =   20.0000      
Z-test statistic= (x̅ - µ )/SE = (   536.000   -   500   ) /    20.0000   =   1.800
                          
  
p-Value   =   0.035930   [ Excel formula =NORMSDIST(z) ]              
Decision:   p-value<α, Reject null hypothesis                       

answer: option B)

B- The prep program resulted in significant improvement in SAT scores