Newspaper headlines at the time and traditional wisdom in the succeeding decades
ID: 3389121 • Letter: N
Question
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-
female(1) male(2) total alive 343 367 710 dead 127 1364 1491 total 470 1731 2201Explanation / Answer
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]