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Chapter 12: Hypothesis Tests – Large Samples
Case I:
Samples of size
n
will be obtained from a normal population with
known standard deviation
. In this case, the sampling distribution for the
sample means will be normally distributed.
Case II:
This case does not require the sampling distribution to be normally
distributed with known standard deviation
. As long as the sample size is
large enough (
> 30) the sampling distribution of the sample means will be
approximately normally distributed.
In both cases we can invoke the
Central Limit Theorem
.
We refer to tests based on the statistic
̅
√ ⁄
or
̅
√ ⁄
as large sample
tests because we are assuming that the sampling distribution for the sample
means is normally or approximately normally distributed. The test requires
that the sample size
> 30 when
is unknown, unless the sampling
population is exactly normally distributed. If the sampling distribution is
normal, the test is appropriate for any sample size.
Figure 12- 10
shows the experimental display of the sampling population
with its mean
and standard deviation
for Case 1 described above.
Recall, for this case the sampling population is assumed to be normally
distributed.