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 the Titanic in greater proportion than men. Heres a table with the relevant data. Does it appear that a higher proportion of women survived? Conduct the appropriate hypothesis test. Use alpha of 0.01

Hypothesis Ho-

Alternative Ha-

Construct a 99% Confidence Interval for the true difference in proportion of men and women that survived the Titanic.

State your conclusion in sentence form-

Solution

t-test For Single Mean
Set Up Hypothesis
Null, H0: U=5
Alternate, H1: U!=5
Test Statistic
Population Mean(U)=5
Sample X(Mean)=6.364
Standard Deviation(S.D)=2.111
Number (n)=11
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =6.364-5/(2.111/Sqrt(10))
to =2.143
| to | =2.143

P-Value :Two Tailed ( double the one tail ) -Ha : ( P != 2.143 ) = 0.0577
Hence Value of P0.1 > 0.0577,Here we Reject Ho

b)
CI = (p1 - p2) ± Z a/2 Sqrt(p1(1-p1)/n1 + p2(1-p2)/n2 )
Proportion 1
No. of chances( X1 )=343
No.Of Observed (n1)=470
P1= X1/n1=0.73
Proportion 2
No. of chances(X2)=367
No.Of Observed (n2)=1731
P2= X2/n2=0.212
C.I = (0.73-0.212) ±Z a/2 * Sqrt( (0.73*0.27/470) + (0.212*0.788/1731) )
=(0.73-0.212) ± 2.58* Sqrt(0.001)
=0.518-0.059,0.518+0.059
=[0.459,0.576]