Question

One​ year, the mean age of an inmate on death row was 39.9 years. A sociologist wondered whether the mean age of a​ death-row inmate has changed since then. She randomly selects 32 death-row inmates and finds that their mean age is 38.3,with a standard deviation of 8.1. Construct a​ 95% confidence interval about the mean age. What does the interval​ imply?

A) Choose the correct hypotheses.

B) Construct a​ 95% confidence interval about the mean age.

The lower bound is ?

The upper bound is?

What does the interval​ imply?

A.Since the mean age from the earlier year is contained in the​ interval, there is not sufficient evidence to conclude that the mean age had changed.

B.Since the mean age from the earlier year is contained in the​ interval, there is sufficient evidence to conclude that the mean age had changed.

C.Since the mean age from the earlier year is not contained in the​ interval, there is not sufficient evidence to conclude that the mean age had changed.

D.Since the mean age from the earlier year is not contained in the​ interval, there is sufficient evidence to conclude that the mean age had changed.

Answer 1

A) Claim: The mean age of a death-row inmate has changed since then.

The null and alternative hypothesis is

B) Sample size = n = 32

Sample mean = = 38.3

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 ( 38.3 - 2.9204 , 38.3 + 2.9204) = > ( 35.3796 , 41.2204)

A. Since the mean age from the earlier year is contained in the interval, there is not sufficient evidence to conclude that the mean age had changed.