Respuesta :
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.
[tex]H_o: \mu = 36.2[/tex], [tex]H_a: \mu \neq 36.2[/tex]
[tex]\mu = 36.2[/tex], [tex]\bar x = 38.9[/tex], [tex]\sigma = 9.6[/tex], n=32
This is a two sided test, with df = 32-1 = 31 and the critical values are [tex]\pm t_{0.025} =\pm2.040[/tex].
Now find the z score as shown:
[tex]z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
Substitute the respective values:
[tex]z=\frac{38.9-36.2}{\frac{9.6}{\sqrt{32}}}[/tex]
[tex]z=\frac{2.7}{\frac{9.6}{5.6568}}}[/tex]
[tex]z=1.59[/tex]
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.
