Question

Review the concepts of confidence interval and margin of error studied in this unit. Say you were researching some aspect of a population, and the sample proportion is 25% with a margin of error of 4% at the 95% confidence level. Does this mean that there is 95% chance that the population proportion is between 21% and 29%? Why or why not, and what might be the implications for your research in either case?

Answer 1

basically the confidence interval of any parameter is the estimated interval for parameter with certain confidence level on the behalf of sample. we can find confidence interval for any parameter as

estimated value of parameter +(-) * margin of error.

here, Margin of error = Critical value x Standard error of the statistic, here statistic is the function of sample observations. therefore,

The margin of error is the range of values below and above the sample statistic in a confidence interval. and the confidence of interval is a way to show what the uncertainty is with a certain statistic.

Margin of Error for a Proportion

z*sqrt(p(hat) *(1-p(hat))/n)

Where:

phat = sample proportion (“P-hat”).

n = sample size

z = z-score, and (1-alpha)*100% C.I is

p(hat) +(-) Margin of error.

now given Margin of error= 4% = 0.04, C.level=95%

p(hat)= 0.25,

hence, 95% C.I is

0.25-0.04, 0.25+0.04 = 0.21,0.29

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hence it mean that there is 95% chance that the population proportion is between 21% and 29%.