A sample of 2,000 union members was selected and asked about their opinions regarding a proposed contract. A total of 1,600 members were in favor of it. A 95% confidence interval estimated that the population proportion was between 0.78 and 0.82. This indicates that about 80 out of 100 similarly constructed intervals would include the population proportion.

True or False

So Equation(1) and Equation(2)  both are not same C.I hence the given statement is false.

Step-by-step explanation:

Given:

total member =2000

Favor member=1600

Mean=1600/2000=0.8

To Find:

C.I of 95 % and it is true for given statement

Solution:

Now to calculate the

C.I=0.8±Z*Sqrt[p(1-p)/n]

C.I=0.8±1.96Sqrt[0.8(0.2)/2000]

C.I=0.8±0.0175

C.I=0.7825 to 0. 8175  Equation(1)

Now

Above C.I should be same when n =100 and  x= 80 So p=x/n=80/100=0.8

Hence

C.I.=p±Z*Sqrt[p(1-p)/n]

C.I=0.8±1.96*sqrt[0.8*0.2/100]

=0.8±1.96*0.04

=0.8±0.0784

Hence C.I.=0.7216 to 0.8784Equation(2)

By comparing

So Equation(1) and Equation(2)  both are not same C.I hence the given statement is false.