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Chapter 12: Hypothesis Tests – Large Samples
Figure 12- 27:
The Mean and Standard Deviation
for the Distribution of the Difference
Between Two Sample Means
If the sampling distributions are normal to begin with, then the sampling
distribution for the difference between the two sample means will be exactly
normally distributed. If the sampling distributions are not normal to begin
with, then we will require both sample sizes to be greater than 30 (as a rule
of thumb).
Also, when
and
are unknown, if the sample sizes are large enough
(
30 and
30), we can estimate the population variances
and
with the sample variances
and
.
These properties can aid us in testing for the difference between two
population means for large samples.
Following is a summary of the tests for the difference between two
population means using the above information.
Summary of Hypothesis Tests
(a) One-tailed (right-tailed)
:
: