Newspaper headlines at the time and traditional wisdom in th

Newspaper headlines at the time and traditional wisdom in the succeeding decades have held that women and children escaped a sunken ship in greater proportion than men. Here\'s a table with the relevant data. Do you think that survival was independent of whether the person was male or female? Defend your conclusion.

Female

Male

Total

Alive

397397

288288

685685

Dead

125125

13631363

14881488

Total

522522

16511651

21732173

Is there evidence of a significant difference between the proportion of males and females who survived at the 0.050.05 level of significance? What are the null and alternative hypotheses to test?

Solution

Null, No difference between the proportion of males and females who survived Ho: p1 = p2
Alternate, difference between the proportion of males and females who survived H1: p1 != p2
Test Statistic
Sample 1 : X1 =397397, n1 =522522, P1= X1/n1=0.761
Sample 2 : X2 =288288, n2 =16511651, P2= X2/n2=0.017
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.04
Q^ Value For Proportion= 1-P^=0.96
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.761-0.017)/Sqrt((0.04*0.96(1/522522+1/16511651))
Zo =2690.547
| Zo | =2690.547
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =2690.547 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != 2690.5471 ) = 0
Hence Value of P0.05 > 0,Here we Reject Ho

We have evidence to indicate difference between the proportion of males and females who survived