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

Explanation:

Formula for margin of error (E):

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

Given: n= 200

`p=(147)/(200)`

Critical value for 97% confidence level = 2.17

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

`=2.17\sqrt{(147)/(200)((53)/(200))}\\\\=2.17* √(0.194775)\\\\=2.17*0.441333207452\approx0.9577`

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