Use Excel) A recent report criticizes SATtestpreparation providers for promising big score gains without any hard data to back up such claims (The Wall Street Journal, May 20, 2009). Suppose eight collegebound students take a mock SAT, complete a threemonth testprep 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. 
Student  Score on Mock SAT  Score on Real SAT 
1  1,868  1,852 
2  1,728  1,787 
3  2,041  2,008 
4  2,009  2,222 
5  1,643  1,691 
6  1,806  1,965 
7  1,945  1,805 
8  1,729  1,775 
Click here for the Excel Data File 
Let the difference be defined as scores on Mock SAT – Real SAT. 
a. 
Specify the competing hypotheses that determine whether completion of the testprep course increases a student’s score on the real SAT. 

b. 
Assuming that the SAT scores difference is normally distributed, calculate the value of the test statistic and its associated pvalue. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Compute the pvalue using your unrounded test statistic value. Round "Test statistic" value to 2 decimal places and "pvalue" to 4 decimal places.) 
Test statistic  
pvalue  
c.  At the 5% significance level, do the sample data support the testprep providers’ claims? 

The table given below ,
Student  Score on Mock SAT(X)  Score on Real SAT(Y)  di=XY  di^2 
1  1868  1852  16  256 
2  1728  1787  59  3481 
3  2041  2008  33  1089 
4  2009  2222  213  45369 
5  1643  1691  48  2304 
6  1806  1965  159  25281 
7  1945  1805  140  19600 
8  1729  1775  46  2116 
Sum  336  99496 
From table ,
Let ,
a) Hypothesis: Vs
b) The test statistic is ,
pvalue=
The Excel function is , =TDIST(1.08,7,1)
c) Decision : Here , pvalue=0.1580 >
Therefore , Do not reject H0 since the pvalue is more than α.
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