Answer: interval proportion = - 0.144, 0.204
Step-by-step explanation: from the question.
X1= 35, n1 = 50, x2= 40, n2= 60
P1=x1/n1=35/50 = 7/10 = 0.7,
1-p1 = 1 - 0.7 =0.3
P2 = x2/n2 = 40/60 = 2/3 = 0.67
1 - p2 = 1 - 0.67 = 0.33
95% confidence interval for population proportion is given as
p1-p2 + Zα/2 * √{p1(1-p1)/n1 + p2(1-p2)/n2}..... This is the upper limit
p1-p2 - Zα/2 * √{p1(1-p1)/n1 + p2(1-p2)/n2}.... This is the lower limit
p1 = first sample proportion = 0.7
p2 = second sample proportion = 0.67
n1 = first sample size = 50
n2= second sample size = 60
Zα/2= z score for a two tailed test at 5% level of significance = 1.96.
Upper limit
(0.7 - 0.67) + 1.96 * {√(0.7*0.3/50 + 0.67*0.33/60)}
0.03 + 1.96 {√(0.0042 + 0.003685)}
0.03 + 1.96 √0.007885
0.03 + 1.96 ( 0.08879)
0.03 + 0.174
= 0.204.
Upper limit
(0.7 - 0.67) + 1.96 * {√(0.7*0.3/50 + 0.67*0.33/60)}
0.03 + 1.96 {√(0.0042 + 0.003685)}
0.03 + 1.96 √0.007885
0.03 + 1.96 ( 0.08879)
0.03 + 0.174
= 0.204.
Lower limit.
Upper limit
(0.7 - 0.67) + 1.96 * {√(0.7*0.3/50 + 0.67*0.33/60)}
0.03 + 1.96 {√(0.0042 + 0.003685)}
0.03 + 1.96 √0.007885
0.03 + 1.96 ( 0.08879)
0.03 + 0.174
= 0.204.
Upper limit
(0.7 - 0.67) + 1.96 * {√(0.7*0.3/50 + 0.67*0.33/60)}
0.03 + 1.96 {√(0.0042 + 0.003685)}
0.03 + 1.96 √0.007885
0.03 + 1.96 ( 0.08879)
0.03 + 0.174
= 0.204.
Upper limit
(0.7 - 0.67) + 1.96 * {√(0.7*0.3/50 + 0.67*0.33/60)}
0.03 + 1.96 {√(0.0042 + 0.003685)}
0.03 + 1.96 √0.007885
0.03 + 1.96 ( 0.08879)
0.03 + 0.174
= 0.204.
Lower limit
(0.7-0.67) - 1.96 * {√(0.7*0.3/50 + 0.67*0.33/60)}
0.03 - 1.96 {√(0.0042 + 0.003685)}
0.03 - 1.96 √0.007885
0.03 - 1.96 ( 0.08879)
0.03 - 0.174
= - 0.144
interval proportion = - 0.144, 0.204