A researcher wonders about the daily health habits of docto

. A researcher wonders about the daily health habits of doctors versus other professionals of similar education. As part of her research, she randomly surveys 100 doctors and 115 other professionals and asks they if they take any daily health supplements (vitamins, herbal supplements, etc.). 36 of the doctors and 45 of the other professionals report taking at least one daily supplement. Does this data support the claim that the behavior of doctors is different than that of other professionals at the = 0.10 level of significance?

Solution

Null, There Is No Significance between them Ho: p1 = p2
Alternate, data support the claim that the behavior of doctors is different than that of other professionals H1: p1 != p2
Test Statistic
Sample 1 : X1 =36, n1 =100, P1= X1/n1=0.36
Sample 2 : X2 =45, n2 =115, P2= X2/n2=0.391
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.377
Q^ Value For Proportion= 1-P^=0.623
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.36-0.391)/Sqrt((0.377*0.623(1/100+1/115))
Zo =-0.472
| Zo | =0.472
Critical Value
The Value of |Z | at LOS 0.1% is 1.645
We got |Zo| =0.472 & | Z | =1.645
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != -0.4725 ) = 0.6366
Hence Value of P0.1 < 0.6366,Here We Do not Reject Ho

we don\'t have evidence to indicate that data support the claim that the behavior of doctors is different than that of other professionals