The data shows that 71% of all shoppers use coupons. 18 times out of 20 these results were considered accurate to within 2.5%. What is the margin of error?

Answer 1

short answer 2.5%

Long answer:

Answering questions like these are always fraught with pitfalls and dangers to those approaching from the outside. So here goes. Assumptions. The proportion of shoppers using coupons is given and assumed to be a population parameter ρ with a value of .71 ± The similar proportion indicating how often results were correct is considered to be the mean value of a large number (well in excess of 20) samples with a value of .9 or 90% to the question of , was the sample mean within the Confidence Interval?. This is the observed long term confidence.

The final assumption is that the 2.5% (.025) accuracy is an absolute accuracy (i.e. the accuracy of the sample p in terms of value of the p) and not reflecting as a percentage of the proportion, which would be a smaller number)

Under these assumptions the span of the 90% confidence interval is given to us as .71 ± .025.

Under the deffinitoin for margin of error (Usually, the margin of error is defined as the radius (half the width) of a confidence interval for a given sample - Wikipedia) and since the width of the confidence interval is 2 times the ± .025, then the margin of error is .025.

The answer is rather simple , as long as the assumptions hold.