# CONFIDENCE INTERVAL ESTIMATION FOR PROPORTION -...

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CONFIDENCE INTERVAL ESTIMATION FOR PROPORTIONConfidence IntervalStatisticians use a confidence interval to express the degree of uncertainty associated with a sample statistic. A confidence interval is an interval estimate combined with a probability statement.Confidence intervals are preferred to point estimates and to interval estimates, because only confidence intervals indicate (a) the precision of the estimate and (b) the uncertainty of the estimate.The formula for a CI for a population proportion isis the sample proportion,n is the sample size, and z*is the appropriate value from the standard normal distribution for your desired confidence level. The following table shows values of z*for certain confidence levels.To calculate a CI for a population proportion:1.Determine the confidence level and find the appropriate z*-value.Refer to the above table for z*-values.2.Find the sample proportion,by dividing the number of people in the sample having the characteristic of interest by the sample size (n).Note:This result should be a decimal value between 0 and 1.3.Multiplyand then divide that amount by n.4.Take the square root of the result from Step 3.5.Multiply your answer by z*This step gives you the margin of error.6.Takeplus or minus the margin of error to obtain the CI; the lower end of the CI isminus the margin of error, and the upper end of the CI isplus the margin of error.Example1For example, suppose you want to estimate the percentage of the time (with 95% confidence) you’re expected to get a red light at a certain intersection. Suppose you take a random sample of 100 different trips through this intersection and .