(Use Excel) A recent report criticizes SAT-test-preparation providers for promis

Question

(Use Excel) A recent report criticizes SAT-test-preparation providers for promising big score gains without any hard data to back up such claims (The Wall Street Journal, May 20, 2009). Suppose eight college-bound students take a mock SAT, complete a three-month test-prep course, and then take the real SAT. Let the difference be defined as Score on Mock SAT minus Score on Real SAT. Use Table 2. Specify the competing hypotheses that determine whether completion of the test-prep course increases a student's score on the real SAT. H_0: mu_D = 0; H_A: mu_D 0 Assuming that the SAT scores difference is normally distributed, calculate the value of the test statistic and its associated p -value. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answers to 2 decimal places.) At the 5% significance level, do the sample data support the test-prep providers' claims? Do not reject H_0 since the p-value is more than a.

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   ud   =   0  
Ha:   ud   =/   0  
At level of significance =    0.01          
As we can see, this is a    two   tailed test.      
              
Calculating the standard deviation of the differences (third column):              
              
s =    76.77100936          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    27.14265066          
              
Calculating the mean of the differences (third column):              
              
XD =    0.25          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    0.009210596          
              
As df = n - 1 =    7          
              
              
Also, using p values, as it is two tailed,              
              
p =        0.992908113 = 0.99 [ANSWER, P VALUE]

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Your answer is very close. Maybe it just wants 0.99 instead of 0.9900, as it says 2 decimal places. If it is marked incorrect, please report this question to your instructor so he can reconsider. Thanks!

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