aSet up the hypotheses to test whether the average life expe

a.Set up the hypotheses to test whether the average life expectancy of female Bostonians is higher than that of male Bostonians

.

b.Calculate the value of the test statistic and its p-value.

c.At the 10% significance level, what is the conclusion? On average, do female Bostonians live longer than male Bostonians?

d.Repeat the hypothesis test using the critical value approach.

Solution

Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 = u2
Alternate,Female Bostonians live longer than male Bostonians - H1: u1 > u2
Test Statistic
X(Mean)=81.1
Standard Deviation(s.d1)=8.2 ; Number(n1)=32
Y(Mean)=74.8
Standard Deviation(s.d2)=8.6; Number(n2)=32
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =81.1-74.8/Sqrt((67.24/32)+(73.96/32))
to =3
| to | =3
Critical Value
The Value of |t a| with Min (n1-1, n2-1) i.e 31 d.f is 1.309
We got |to| = 2.99915 & | t a | = 1.309
Make Decision
Hence Value of | to | > | t a| and Here we Reject Ho
P-Value:Right Tail -Ha : ( P > 2.9992 ) = 0.00265
Hence Value of P0.1 > 0.00265,Here we Reject Ho

We have evidence to cliam that Female Bostonians live longer than male Bostonians