Read the stated facts first. Check that the observations form an appropriately independent random sample from the relevant population. The first decision flowchart has two panels: justify the sample-mean model, then check variance information if a mean test is required.
Population shape and sample size
Population stated
to be normal?
Exact normal mean
at any sample size.
Go to panel 2 for a test.
Sample sufficiently
large for CLT?
Approximately normal mean.
Population normality
is unnecessary.
Go to panel 2 for a test.
Population explicitly
non-normal?
Small non-normal sample:
normal mean model is
not justified here.
Shape unknown: assume
a normal population
if reasonable in context.
Then go to panel 2.
Variance information for a mean test
Population
variance known?
Use the known variance.
Exact or approximate test
as justified in panel 1.
Sample sufficiently
large?
Use an unbiased
variance estimate.
Large-sample approximate test.
Small sample + unknown
population variance:
H2 normal mean test
not justified by normality alone.
Bridge the decision
Compare a small sample with known population variance, a large sample with estimated variance, and a small sample with estimated variance. The first needs supplied or reasonable assumed population normality. The second uses a large-sample approximation. The third is not justified as a current H2 normal mean test merely by assuming normality.
For a sample-mean probability question, stop after panel 1 and use the supplied or otherwise justified variance information. For a test, continue to panel 2. State only the missing conditions, distinguish exact from approximate normality, and give the reason that applies to this question.

Read the stated facts first. Check that the observations form an appropriately independent random sample from the relevant population. The first decision flowchart has two panels: justify the sample-mean model, then check variance information if a mean test is required.

Exact normal mean
at any sample size.
Go to panel 2 for a test.

Approximately normal mean.
Population normality
is unnecessary.
Go to panel 2 for a test.

Small non-normal sample:
normal mean model is
not justified here.

Shape unknown: assume
a normal population
if reasonable in context.
Then go to panel 2.

Use the known variance.
Exact or approximate test
as justified in panel 1.

Use an unbiased
variance estimate.
Large-sample approximate test.

Small sample + unknown
population variance:
H2 normal mean test
not justified by normality alone.

Compare a small sample with known population variance, a large sample with estimated variance, and a small sample with estimated variance. The first needs supplied or reasonable assumed population normality. The second uses a large-sample approximation. The third is not justified as a current H2 normal mean test merely by assuming normality.

For a sample-mean probability question, stop after panel 1 and use the supplied or otherwise justified variance information. For a test, continue to panel 2. State only the missing conditions, distinguish exact from approximate normality, and give the reason that applies to this question.

Deciding Which Mean-Test Assumptions Are Needed

Deciding Which Mean-Test Assumptions Are Needed