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An accounting firm wants to know how many tax payers will wait until the last day to file their taxes. A group of 1000 tax filers were randomly surveyed, revealing that 100 of them said it was likely that they would not file until the last day. Based on this information, a 95% confidence statement indicated that the percentage of tax filers who would file on the last day was estimated to be between 8% and 12% of all tax filers. In this problem, which of the following is the margin of error?


a 1%

b 2%

c 3%

d 4%



If random samples are selected from a population, what happens to the margin of error if the sample size is increased from 100 to 400?

a the margin of error increases

b the margin of error decreases

c the margin of error stays the same

Respuesta :

Using confidence interval concepts, it is found that:

  • The margin of error is of b) 2%.
  • Increasing the sample size, b) the margin of error decreases.

What is the margin of error of a confidence interval and how it relates to the sample size?

Given a confidence interval with two bounds a and b, the margin of error is half the difference of the two bounds.

So, for an interval that is (8%, 12%), the margin of error is given by:

M = (12 - 8)/2 = 2%.

Which means that for the first question, option B is correct.

Additionally, an increase in the sample size results in a decrease of the margin of error, which means that for the second question, option B is also correct.

More can be learned about confidence interval concepts at https://brainly.com/question/25890103

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