Title: Statistics 300: Elementary Statistics
1Statistics 300Elementary Statistics
2Section 9-3 concernsConfidence
IntervalsandHypothesis tests forthe difference
of two means, (m1 m2)
3What is the variance of
- Apply the new concept here also
4Application Use sample values
5Alternative approach when two samples come from
populations with equal variances
homogeneous variances or homoscedastic
6When samples come from populations with equal
variances
7When samples come from populations with equal
variances
8Alternative notation for thepreceding formula
9When doing confidence intervalsof hypothesis
tests involving (m1 m2) one must first decide
whether the variances aredifferent or the
same,heterogeneous or homogeneous.
10If the variances are different(heterogeneous),
then use thefollowing expression as partof the
confidence interval formulaor the test statistic
11If the variances are the same(homogeneous), then
use thisalternative expression as partof the
confidence interval formulaor the test statistic
12When the variances are pooledto estimate the
common (homogeneous) variance, then the degrees
of freedom for both samples are also pooled by
adding them together.
13Application to CI(m1 - m2)
14Application to CI(m1 - m2)when variances are
different
In this case, the degrees of freedom for t will
be the smaller of the two sample degrees of
freedom.
15Application to CI(m1 - m2)when variances are the
same
In this case, the degrees of freedom for t will
be the sum of the two sample degrees of freedom.
16Tests concerning (m1 - m2)Test Statistic
17Test statistic for (m1 - m2)when variances are
different
In this case, the degrees of freedom for t will
be the smaller of the two sample degrees of
freedom.
18Test statistic for (m1 - m2)when variances are
the same
In this case, the degrees of freedom for t will
be the ssum of the two sample degrees of freedom.
19Section 9-3Handling Claims / Hypotheses
- Write the claim in a symbolic expression as
naturally as you can - Then rearrange the expression to have the
difference between the two means on one side of
the relational operator (lt gt )
20Section 9-3Handling Claims / Hypotheses
- Statement Mean 2 is less than four units more
than Mean 1 - So
- Rearrange
- H0
- H1
21Section 9-3Handling Claims / Hypotheses
- Statement On average, treatment A produces 18
more than treatment B - So
- Rearrange
- H0
- H1