A surveyor wants to estimate the percentage of maple trees among all trees in a

Question

A surveyor wants to estimate the percentage of maple trees among all trees in a large national forest. It would be impossible to find the actual percentage (too time consuming). Instead the surveyor selects several areas at random and determines the percentage of maple tress in the selected sample to be about 30%. The number of trees in the sample was 400. The surveyor can be about 95% confident that the percentage of maple trees in the national forest is between_______ % and___ %.

please show the work

Explanation / Answer

Ans:

sample proportion=0.3

sample size=400

z value for 95% confidence interval is 1.96

95% confidence interval of true proportion

=0.3+/-1.96*sqrt(0.3*(1-0.3)/400)

=0.3+/-0.045

=(0.255, 0.345)

The surveyor can be about 95% confident that the percentage of maple trees in the national forest is between 25.5% and 34.5%.

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