In a recent poll, 320 people were asked if they liked dogs, and 62% said they did. Find the Margin of Error for this poll, at the 99% confidence level.

Question

Give your answer to four decimal places if possible.

Answer 1

To calculate the margin of error, first we need to find the confidence interval for a proportion (% of a total).

The formula is p +/- Z_∝/2 √((p * (1-p)) / n)

If 62% like dogs, then p = 0.62 (although exact p is 0.61875 or 61.875%)

If you want 99% confidence, then ∝ = 0.01, so we look up Z_0.01/2 = Z_0.005 => 2.585

https://sites.berry.edu/vbissonnette/wp-content/uploads/sites/21/2015/07/z.pdf

Now enter p and Z_∝/2 into the formula...

= p +/- Z_∝/2 √((p * (1-p)) / n)

= 0.62 +/- 2.585 √((0.62 * 0.38) / 320)

= 0.62 +/- 2.585 √(0.2356 / 320)

= 0.62 +/- 2.585 √(0.000736)

Note: In your calculator, you can take the square root by using X^Y and making Y = 0.5, or 0.000736^0.5

= 0.62 +/- 2.585 * 0.02713

= 0.62 +/- 0.0701

The question asks for the margin of error, so 0.0701 would be the final answer to 4 decimal places.

If you want to finish you the formula, add and subtract that from 0.62

99% confidence interval would be (0.5499, 0.6901), although I'm suspicious of this poll that only 62% liked dogs. This seems really low to me!

Note: results may vary slightly based on how much rounding you do in the formulas.