Question

In a random sample of 2500 sports fans, 61% prefer basketball over soccer.

Answer 1

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The Margin of error in this survey is 1%.

What is the margin of error?

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The wider the margin of error, the less confident one should be that a poll result reflects the outcome of a population-wide survey.

The random sample of 2500 sports fans, out of which 61% prefer basketball over soccer, therefore, we can write n=2500 and p=0.61. Thus, the margin of error can be written as,

$MOE=\sqrt{\dfrac{\hat p(1-\hat p)}{n}} = \sqrt{\dfrac{0.61(1-0.61)}{2500}} = 0.00975 = 0.975\% \approx 1\%$

Hence, the Margin of error in this survey is 1%.

Learn more about Margin of Error:

brainly.com/question/13990500

#SPJ1