Question

In sample of 200 economists, 147 choose the FRED database as the most popular economic database. Calculate the margin of error for a 97% confidence interval.

Answer 1

Answer: 0.9577

Step-by-step explanation:

Formula for margin of error (E):

$E= z^*\sqrt{\dfrac{p(1-p)}{n}}$ , where p = sample proportion, n =sample space, z* critical z-value.

Given: n= 200

$p=\dfrac{147}{200}$

Critical value for 97% confidence level = 2.17

Margin of error (E) = $2.17\sqrt{\dfrac{147}{200}(1-\dfrac{147}{200})}$

$=2.17\sqrt{\dfrac{147}{200}(\dfrac{53}{200})}\\\\=2.17\times \sqrt{0.194775}\\\\=2.17\times0.441333207452\approx0.9577$

Hence, the margin of error for a 97% confidence interval = 0.9577