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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%.
<h3>What is the margin of error?</h3>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,
Hence, the Margin of error in this survey is 1%.
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Answer with Step-by-step explanation:
Let
Substitute n=2
Then
Hence, P(n) is true for n=2
Suppose that P(n) is true for n=k >1
Now, we shall prove that p(n) is true for n=k+1
LHS
Substitute the value of P(k)
LHS=RHS
Hence, P(n) is true for all n >1.
Hence, proved