TWOSAMPLE tTESTS the sample sizes get much smaller so use th

TWO-SAMPLE t-TESTS (the sample sizes get much smaller, so use the second formula in the lecture notes for the t-test) PLEASE SHOW ALL WORK AND CURVE DIAGRAM Use t when s1 , s2 are unknown AND samples are small (n1 + n2 < 32)\\

A professor claims that the average of scores obtained by History majors is close to the average of scores obtained by the Science majors.At = .1 is there enough evidence to support the claim?

History majors:Average score = 80       standard deviation = 5               n1 = 15

Science majors:Average score = 83           standard deviation = 4          n2 = 11

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)=80
Standard Deviation(s.d1)=5 ; Number(n1)=15
Y(Mean)=83
Standard Deviation(s.d2)=4; Number(n2)=11
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =80-83/Sqrt((25/15)+(16/11))
to =-1.7
| to | =1.7
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 10 d.f is 3.169
We got |to| = 1.69809 & | t | = 3.169
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -1.6981 ) = 0.12
Hence Value of P0.01 < 0.12,Here We Do not Reject Ho