Question

The average age of an inmate in death row in 1989 was 36.2 years of age. A Sociologist claims that the average age of death-row inmates has changed since. The sociologist collects a sample of 32 death-row inmates and finds that their mean age is 38.9 with a standard deviation of 9.6 years. Test the Sociologist’s claim at 0.05 significance level.

Answer 1

Answer:

We will not reject the null hypothesis.

There is not enough evidence to  support the claim that the mean age of death -row inmates is different from 36.2 years.

Step-by-step explanation:

Consider the provided information.

The average age of an inmate in death row in 1989 was 36.2 years of age.

The sociologist collects a sample of 32 death-row inmates and finds that their mean age is 38.9 with a standard deviation of 9.6 years. Test the Sociologist’s claim at 0.05 significance level.

From the above information.

$H_o: \mu = 36.2$, $H_a: \mu \neq 36.2$

$\mu = 36.2$, $\bar x = 38.9$, $\sigma = 9.6$, n=32

This is a two sided test, with df = 32-1 = 31 and the critical values are $\pm t_{0.025} =\pm2.040$.

Now find the z score as shown:

$z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}$

Substitute the respective values:

$z=\frac{38.9-36.2}{\frac{9.6}{\sqrt{32}}}$

$z=\frac{2.7}{\frac{9.6}{5.6568}}}$

$z=1.59$

Since, 1.591 doesn’t lie in the critical region,  hence we will not reject the null hypothesis.

There is not enough evidence to  support the claim that the mean age of death -row inmates is different from 36.2 years.