You wish to test H0 mu1 mu2 versus Ha mu1mu2 at a significa

You wish to test H0 :mu1 = mu2 versus Ha: mu1>mu2 at a significance level of Alpha= 0.05. You obtain a sample of size n1 = 18 with a mean of x1 = 88.2 and a standard deviation of s1= 13.3 from the first population. You obtain a sample of size n2= 11 with a mean of x2 = 71.8 and a standard deviation of S2 = 11. 5from the second population. What is the test statistic?

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)=88.2
Standard Deviation(s.d1)=13.3 ; Number(n1)=18
Y(Mean)=71.8
Standard Deviation(s.d2)=11.5; Number(n2)=11
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =88.2-71.8/Sqrt((176.89/18)+(132.25/11))
to =3.51