Question
One year, the mean age of an inmate on death row was 38.938.9 years. A sociologist...
One year, the mean age of an inmate on death row was
38.938.9
years. A sociologist wondered whether the mean age of a death-row inmate has changed since then. She randomly selects
3232
death-row inmates and finds that their mean age is
37.837.8,
with a standard deviation of
8.18.1.
Construct a 95% confidence interval about the mean age. What does the interval imply?
LOADING...
Click the icon to view the table of critical t-values.
Choose the correct hypotheses.
Upper H 0H0:
▼
muμ
pp
sigmaσ
x overbarx
▼
equals=
less than<
greater than>
not equals≠
nothing
Upper H 1H1:
▼
sigmaσ
x overbarx
pp
muμ
▼
not equals≠
greater than>
less than<
equals=
nothing
(Type integers or decimals. Do not round.)
Homework Answers
Answer #1
Sample size = n = 32
Sample mean = 
= 37.8
Standard deviation = s = 8.1
We have to construct 95% confidence interval.
Formula is
Here E is a margin of error.
Degrees of freedom = n - 1 = 32 - 1 = 31
Level of significance = 0.05
tc = 2.040 ( Using t table)
So confidence interval is ( 37.8 - 2.9204 , 37.8 + 2.9204) = > ( 34.88 , 40.72)
--------------------------------------------------------------------------------------------------------------------
Claim: The mean age of a death-row inmate has changed.
The null and alternative hypothesis is
The value 38.9 belongs to the above interval so we fail to reject the null hypothesis.
Conclusion: The mean age of a death-row inmate has NOT changed.
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