3.-12 General K. is concerned about sexually transmitted disease (STD) among the
troops. In random inspection of 100 soldiers, 31 were found to have a veneral
disease. To reduce the incidence, soldiers were shown an educational film on
preventing STDs. In a second inspection of 200 soldiers, 43 had STDs. Calculate
the following statistics.
Soldiers with STDs
What
What
What
What
What
is
is
is
is
is
the
the
the
the
the
1st Inspection
Sample proportion (mean)
31
Standard deviation
Standard error of the proportion estimate
Overall standard error
t-score
2nd Inspection
43
What do these statistics suggest?
Solution:
Let ‘x1’ denote the number of soldiers having veneral disease.
Let ‘x2’ denote the number of soldiers having veneral disease after the film was
shown
X1 = 31
N1 = 100
X2 = 43
N2 = 200
SAMPLE PROPORTION:
P1 = proportion of soldiers having disease before seeing film = 31 /100 = 0.31
P2 = proportion of soldiers having disease after seeing film = 43 /200 = 0.215
STANDARD DEVIATION :
p1(1-p1)/n1
for x1
p2(1-p2)/n2
for x2
For x1:
0.31*0.69 /100 = 0.046
For x2:
0.215*0.785/200 = 0.029
PORPORTION ESTIMATE:
P = (n1p1+n2p2)/ (n1+n2)
P = (100*0.31 + 200 *0.215)/ (100+200)
P = 0.247
Q = 1-P = 1-0.247 = 0.753
STANDARD ERROR OF THE PROPORTION ESTIMATE:
SE(P) =  PQ(1/N1+1/N2)
= 0.247*0.753 ( 1/100 + 1/200)
= 0.247*0.753 * 0.015
= 0.053
OVERALL STANDARD ERROR:
0.053
T SCORE:
t = (p – P)/ SE (P)
t = (0.31 – 0.247) / 0.053 = 1.1886
Also
t = (0.215 – 0.247) / 0.053 = - 0. 6038
Proportion of soldiers after seeing the film is less than the proportion of soldiers
before seeing the film.