Answer :
Answer:
Construct a 98% confidence interval for the difference between the population proportions p1 - p2 is ( 0.110199 and 0.309801)
Step-by-step explanation:
Given data
sample n1 = 300 women
sample n2 = 200 men
control legislation f1 = 49% = 0.49
control legislation f2 = 28% = 0.28
to find out
Construct a 98% confidence interval for the difference between the population proportions p1 - p2
solution
we know difference of control legislation = f1 -f2
so difference is 0.49-0.28 = 0.21
so for 98% confidence Z value is 2.326 from standard table
and interval for difference formula is
f1 - f2 - Z [tex]\sqrt{f1(1-f1)/n1 + f2(1-f2)/n2}[/tex]
and
f1 - f2 + Z [tex]\sqrt{f1(1-f1)/n1 + f2(1-f2)/n2}[/tex]
put all these value and we get difference of population proportion are
0.49 - 0.28 - 2.326 [tex]\sqrt{0.49(1-0.49)/300 + 0.28(1-0.28)/200}[/tex]
and
0.49 - 0.28 + 2.326 [tex]\sqrt{0.49(1-0.49)/300 + 0.28(1-0.28)/200}[/tex]
= 0.110199
and
= 0.309801
Construct a 98% confidence interval for the difference between the population proportions p1 - p2 is ( 0.110199 and 0.309801)