HW4 SOLUTIONS
Inference for Population Mean
1. List all the assumptions that need met in order for a
t
distribution based inference to be valid.
Correct:
data must be from a random sample from a large population
observations within the sample must be independent
n small - population distribution must be approximately normal
n large - population distribution need not be approximately normal (CLT kicks in)
2. The blood pressure (average of systolic and diastolic measurements) of each of 38 randomly
selected persons was measured. The average was 94.5 mm Hg and the standard deviation 8.0497 mm Hg.
a. Construct a 95% confidence interval for the true mean blood pressure.
Correct:
TI-84
STAT->TESTS and T-interval->Enter->Stats->Enter->Scroll down to enter sample mean, sample sd, and
sample size, C-Level: .95->highlight Calculate->Enter
yields (91.854, 97.146)
b. Interpret the interval you just computed in part (a).
Correct:
We are 95% confident that true mean blood pressure for people like the ones used in this study is at least
91.854 mm Hg and at most 97.146 mm Hg.
c.
Use the QQplot to comment on whether it appears the assumption of normality has been violated.
Correct:
Goal:
We need to check the assumption that
ݔ̅
has a
normal distribution.
We get that one of two ways:
1)
Either the data that created
ݔ̅
is from a normal
distribution
2)
Or the sample size is large enough for the CLT to
“kick in”
Step 1 – Check the QQ plot
I see no systematic departure from the line, except for
that little blip in the upper end of the distribution.
Step 2 – Can we call the CLT?
Mainly, the points form a linear pattern and our sample
size is 38, so the CLT should kick in anyway.
Conclusion
: I do not see evidence against normality of
ݔ̅
- it
should be just fine to proceed with this
t
distribution
based procedure.

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