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

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.

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 \\eq 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=(\bar x-\mu)/((\sigma)/(√(n)))`

Substitute the respective values:

`z=(38.9-36.2)/((9.6)/(√(32)))`

`z=(2.7)/((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.