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In an ecological study, the sampling mean proportion is 0.28 and the sample size is 50. What is the margin of error with a confidence level of 95%?

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In an ecological study, the sampling mean proportion is 0.28 and the sample size is 50. a) What is the margin of error with a confidence level of 95%?
The solution to a system of two linear equations is (4, -3). One equation has a slope of 4. The slope of the other line is the negative reciprocal of the slope of the first. The system described above is represented by the following equations: y --X-2 y - 4x - 19 Please select the best answer from the choices provided

The margin of error is 0.1245 (approx) with a confidence level of 95%.

What is margin of error ?

Margin of error is a statistic which is expressing the measurement of random sampling error in the results of a survey.

Margin of error = [tex]z^{*}[/tex][tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

where [tex]z^{*}[/tex] is the value for confidence level or quantile,

p is the sampling mean proportion and n is the sample size.

How to find margin of error in given problem ?

Here, The sampling mean proportion(p)= 0.28

The sample size(n)= 50

Confidence level = 95%

Hence Value for 95% confidence level ([tex]z^{*}[/tex])= 1.96

∴ Margin of error = [tex]1.96[/tex][tex]\sqrt{\frac{0.28(1-0.28)}{50} }[/tex]

                            = [tex]1.96[/tex][tex]\sqrt{\frac{0.28*0.72}{50} }[/tex]

                            = [tex]1.96\sqrt{\frac{0.2016}{50} }[/tex]

                            = [tex]1.96\sqrt{0.004032}[/tex]

                            = [tex]1.96[/tex]×[tex]0.0635[/tex]

                            = [tex]0.1245[/tex] (approx)

So, The margin of error is 0.1245 (approx).

Learn more about margin of error here :

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