Question

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?

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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.)

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)

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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.