The College Board SAT college entrance exam consists of thre

The College Board SAT college entrance exam consists of three parts: math, writing and critical reading (The World Almanac 2012). Sample data showing the math and writing scores for a sample of twelve students who took the SAT follow.

Click on the webfile logo to reference the data.

a. Using a .05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores? Enter negative values as negative numbers. Round your answer to two decimal places.

What is the p-value? Round your answer to four decimal places.

Solution

Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 = u2
Alternate Hypothesis, There Is Significance between them - H1: u1 != u2
Test Statistic
X(Mean)=514
Standard Deviation(s.d1)=68.274 ; Number(n1)=12
Y(Mean)=489
Standard Deviation(s.d2)=93.466; Number(n2)=12
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =514-489/Sqrt((4661.33908/12)+(8735.89316/12))
to =0.75
| to | =0.75
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 11 d.f is 2.201
We got |to| = 0.74821 & | t | = 2.201
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 0.7482 ) = 0.47
Hence Value of P0.05 < 0.47,Here We Do not Reject Ho