Depression engulfs millions of Americans every day A new fed

Depression engulfs millions of Americans every day. A new federal study reported that 10.9% of adults aged 18–24 identified with some level of depression versus 6.8% of adults aged 65 or older ( The Boston Globe , October 18, 2010). Suppose 250 young adults (18–24 years old) and 200 older adults (65 years old and older) responded to the study.

a. Develop the appropriate null and alternative hypotheses to test whether the proportion of young adults suffering from depression is greater than the proportion of older adults suffering from depression.

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

c. At the 5% significance level, what is the conclusion? Do the sample data suggest that young adults suffer more from depression than older adults?

Solution

Null , There Is No Significance between them Ho: p1 = p2
Alternate, proportion of young adults suffering from depression is greater H1: p1 > p2
Test Statistic
Sample 1 : X1 =27.25, n1 =250, P1= X1/n1=0.109
Sample 2 : X2 =13.6, n2 =200, P2= X2/n2=0.068
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.091
Q^ Value For Proportion= 1-P^=0.909
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.109-0.068)/Sqrt((0.091*0.909(1/250+1/200))
Zo =1.504
| Zo | =1.504
Critical Value
The Value of |Z | at LOS 0.05% is 1.645
We got |Zo| =1.504 & | Z | =1.645
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Right Tail -Ha : ( P > 1.5043 ) = 0.06625
Hence Value of P0.05 < 0.06625,Here We Do not Reject Ho

proportion of young adults suffering from depression is greater than the proportion
of older adults suffering from depression

ANSWER:
a. Ho: p1 = p2 , H1: p1 > p2
b. Zo =1.504
c. No, we don\'t have evidence to support