Question

3. A newspaper in a large city asked 500 women the following: "Do you use organic food products (such as milk, meats, vegetables, etc.)?"

280 women answered "yes." Compute the margin of error. Interpret the resulting interval in context.

Answer 1

Margin of error = 0.0444

The resulting interval = 0.5156 to 0.6044

Explanation:

Data provided in the question:

Sample size, n = 500

Number of women answer yes = 280

Probability of women answering yes, p = 280 ÷ 500

= 0.56

Now,

Margin of error is given as:

E =
`2\sqrt{(p(1-p))/(n)}`

on substituting the respective values, we get

E =
`2\sqrt{(0.56(1-0.56))/(500)}`

or

E = 2 × 0.0222

or

E = 0.0444

And,

The resulting interval

= p ± E

= 0.56 ± 0.0444

= 0.5156 to 0.6044