Answer:
The answer is "(0.782, 0.818)".
Step-by-step explanation:
computing the sample proportion:
[tex]p=\frac{x}{n}= \frac{1,600}{2000}=0.80 \\\\[/tex]
[tex]\text{Computing the} \ 95\% \ \ C.I \\\\[/tex]
[tex]C.I= p \pm Z_{\frac{\alpha}{2}}\sqrt{\frac{P(1-p)}{n}}[/tex]
   [tex]= 0.80 \pm 1.96 \sqrt{\frac{0.80(1-0.80)}{2000}} \\\\= 0.80 \pm 1.96 \sqrt{\frac{0.80(0.20)}{2000}} \\\\= 0.80 \pm 1.96 \sqrt{\frac{0.16}{2000}} \\\\ = 0.80 \pm 1.96 \sqrt{0.00008} \\\\=0.80 \pm 0.18 \\\\= (0.782, 0.818)[/tex]
conclusion:
Since the interval calculation contains higher values than 75 percent of its union membership, the merger proposal is likely to pass.
