Answer: 0.9577
Step-by-step explanation:
Formula for margin of error (E):
[tex]E= z^*\sqrt{\dfrac{p(1-p)}{n}}[/tex] , where p = sample proportion, n =sample space, z* critical z-value.
Given: n= 200
[tex]p=\dfrac{147}{200}[/tex]
Critical value for 97% confidence level = 2.17
Margin of error (E) = [tex]2.17\sqrt{\dfrac{147}{200}(1-\dfrac{147}{200})}[/tex]
[tex]=2.17\sqrt{\dfrac{147}{200}(\dfrac{53}{200})}\\\\=2.17\times \sqrt{0.194775}\\\\=2.17\times0.441333207452\approx0.9577[/tex]
Hence, the margin of error for a 97% confidence interval = 0.9577
