Finally can we support the claim that the life expectancy in

Finally, can we support the claim that the life expectancy in the United States is greater than the life expectancy in Ireland? Specify the answer by (Yes or No)

Also, please specify your answer for all sections.

Solution

Set Up Hypothesis
Null, the life expectancy in the United States is less than the life expectancy in Ireland Ho: u1 < u2
Alternate, the life expectancy in the United States is greater than the life expectancy in Ireland - H1: u1 > u2
Test Statistic
X(Mean)=77.7
Standard Deviation(s.d1)=6.7 ; Number(n1)=245
Y(Mean)=76.2
Standard Deviation(s.d2)=5.1; Number(n2)=260
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =77.7-76.2/Sqrt((44.89/245)+(26.01/260))
to =2.82
| to | =2.82
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 244 d.f is 2.342
We got |to| = 2.81836 & | t | = 2.342
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value:Right Tail -Ha : ( P > 2.8184 ) = 0.00261
Hence Value of P0.01 > 0.00261,Here we Reject Ho