In 2002, the mean age of inmates on death row was 43.7 years (Data from the Depa

Question

In 2002, the mean age of inmates on death row was 43.7 years (Data from the Department of justice sociologist claims that this number has changed since then. She randomly selected 27 inmates on deat row and finds that their mean age is 48.5 years. Can you support the sociologist claim at a 0.1 level of significance? Assuming that the distribution inmates age on death row is normal with a known population standards deviation of 12.9 years. .(Please write all pertinent steps and provide a sketch for the rejected region)

Explanation / Answer

Given that,
population mean(u)=43.7
standard deviation, =12.9
sample mean, x =48.5
number (n)=27
null, Ho: =43.7
alternate, H1: !=43.7
level of significance, = 0.1
from standard normal table, two tailed z /2 =1.645
since our test is two-tailed
reject Ho, if zo < -1.645 OR if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 48.5-43.7/(12.9/sqrt(27)
zo = 1.93345
| zo | = 1.93345
critical value
the value of |z | at los 10% is 1.645
we got |zo| =1.93345 & | z | = 1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != 1.93345 ) = 0.05318
hence value of p0.1 > 0.05318, here we reject Ho
ANSWERS
---------------
null, Ho: =43.7
alternate, H1: !=43.7
test statistic: 1.9335
critical value: -1.645 , 1.645
decision: reject Ho
p-value: 0.05318

we have evidence to support the claim.

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