STATISTICS 301 TA: Perla E. Reyes DISCUSSION 12 Pag. 1
Review
Comparing Two Populations Means
1. Case 1 Normal Populations with Equal Variances
We assume that the two populations have the same variance,
σ2
X=σ2
Y
We call this common value of the variance σ2. We estimate σ2by the po oled sample
variance
s2
p=(n1−1)s2
X+ (n2−1)s2
Y
n1+n2−2.
(a) Confidence Interval for (µX−µY),
1. Compute the sample means ¯x, ¯yand pooled sample variance s2
p.
2. Find taccording to the confidence level and n1+n2−2 degrees of freedom from
Table A.6 (page 655).
Remember when the number of degrees of freedom is greater than 30, go directly to
the ∞row of Table A.6.
3. The C.I. then is
(¯x−¯y)±tspr1
n1
+1
n2
.
(b) Hipotesis Testing for (µX−µY),,
Step 1. Null hypothesis: H0:µX=µY.
There are 3 choices for the alternative hypothesis :
(>): H1:µX> µY.
(<): H1:µX< µY.
(6= ): H1:µX6=µY.
Step 2. Test Statistic
t1=(¯x−¯y)
spp(1/n1) + (1/n2)
Step 3,4. The p-value.
(>): P=P(tn1+n2−2≥t1), which is the area under t-curve with n1+n2−2 degrees
of freedom to the right of t1.
(<): P=P(tn1+n2−2≤t1), which is the area under t-curve with n1+n2−2 degrees
of freedom to the right of −t1.
(6= ): P= 2P(tn1+n2−2≥ |t1|), which is twice the area under t-curve with n1+n2−2
degrees of freedom to the right of |t1|.
Practice Problems
1. Section 16.2 Extra Homework, problems 56 and 54(e).
2. Last Week’s Homework. Questions? What about Section 15.3 Extra Homework, problem 52
or problem 53?
3. Do we have time? Section 16.2 Extra Homework, problem 58.