Question

Choose the best answer

Which of the following best explains what is the margin of error in a test or questionnaire?

a. A statistic that tells us how many points the results may vary.

b. A numerical index that illustrates the level of dispersion of a group.

c. A data that expresses quantitatively the average of some scores.

d. A statistic that demonstrates the level or degree of reliability.

Answer 1

Answer: (a)

Explanation:

In a statistical hypothesis test, one estimates some real attribute of a population, e.g. mean or median, based on a random sample drawn from the population. That is to say, whenever one has to guess about the real population based on a sample statistic, they can assume that the true value will lie near the sample statistic's value. But it is important to know how much the true value can vary. A confidence interval gives this answer stating that in 95% or 90% of cases the true value will remain within a given boundary. The margin of error is a crucial statistic derived from the random sample at hand that determines the range of values above or below the sample statistic or in other words, how many percentage points the results will vary from the real population value.

As far as the formula is concerned, it is as follows: margin of error = critical value*standard error.

Example:

If one wishes to determine the percentage of adult males in the U.S. that takes a certain pill daily. In order to find that, one might want to devise a sample design where only 1% error is allowed 95% of the time, which means the estimated value will not differ from the true value more than 1% in 95 out of 100 times a random sample is drawn from the same population. Here, 1% is the margin of error for the test on the population of all adult males in the U.S.