Confidence Intervals and Hypothesis Tests: Two Samples - Florida ...

Step 1 Gather Data for the Problem, Calculate X1 − X 2 , and Calculate
Step 2 Find / 2
Step 3 Find E =
tα using n1 + n2
− 2 as the degrees of freedom
S S
2 2
p p
α / 2 +
n1 n2
t
⎡⎣ ( X − X ) − E,( X − X ) + E⎤⎦
Step 4 Form 1 2 1 2
S
2
p
=
STATSprofessor.com
Chapter 9
( − 1) + ( −1)
n s n s
2 2
1 1 2 2
n + n − 2
1 2
9.4 t-Test to Compare Two Population Means: Independent Samples (Equal Variances)
Small-Sample Hypothesis Test of: H : ( µ − µ ) = D , H : ( µ − µ ) ≤ D , or : ( µ µ )
0 1 2 0
0 1 2 0
H − ≥ D
0 1 2 0
We will use the same seven steps as always; however, we will need a new t-test statistic. If we assume
equal variances, the test statistic for these problems will be:
The equal variance case
Steps:
( − ) − ( − 1) + ( −1)
X X D n s n s
t = where S =
1 2
2 2
0 2 1 1 2 2
,
2 2
p
S n1 n2
2
p S
+ −
p
+
n n
1 2
1. Express the original claim symbolically
2. Identify the Null and Alternative hypothesis
3. Record the data from the problem
4. Calculate the test statistic*
5. Determine your rejection region
6. Find the initial conclusion
7. Word your final conclusion
, and d.f.= n1 + n2
− 2
7