Margin of Error

Question

A pet supply company wants to find out how satisfied their customers are with their service and inventory.

Assume that a survey was conducted of 500 people and 472 customers said that they were satisfied with the service.

1. Find the margin of error for the sample.

Answer 1

You seem to be missing a confidence level. So let's assume a CL of 95%.

My source is (https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/hypothesis-testing/margin-of-error/).

The formula is a little different for proportions:

Where:

 = sample proportion (“P-hat”).

n = sample size

z = z-score

Step one: Find P-hat by dividing the number of people who responded positively by the sample size. “Positively” in this sense doesn’t mean that they gave a “Yes” answer; It means that they answered according to the statement in the question. 

In your example: 472 / 500 = 0.944

Step two:  Find the z-score that goes with the given confidence interval. Reference (https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/find-critical-values/#CommonCI). A 95% confidence interval has a z-score (a critical value) of 1.96.

So:

z is 1.96.

n is 500.

p-hat is 0.944

solve the equation:

MoE = z * square root (p-hat * (1 - p-hat) / n)

MoE = 1.96 * square root (0.944 * (1-0.944) / 500)

MoE = 1.96 * square root (0.944 * 0.056 / 500)

MoE = 1.96 * square root (0.052864 / 500)

MoE = 1.96 * square root (0.000105728)

MoE = 1.96 * 0.0102824121683582

MoE = 0.020135527849982

Turn this result into a percentage and you get a 2% (2.01%) margin of error.