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Question 507:



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  1. To compute the confidence interval around a proportion we need to find the standard error of the proportion and multiply this times the critical value from the z-distribution for a 2-sided 95% confidence interval--which is 1.96--you can look this up using the percentile to z-score calculator
    1. The standard error of the mean (SEM)  is made up of the standard deviation divided by the square root of the sample size. In a proportion we find the sd by multiplying the proportion for p times the proportion against. So pq = .6*.4 = .24 (this is the variance). Now we take the square root of this to get the standard deviation =.4898.
    2. The square root of the sample size is SQRT(500) = 22.36
    3. The SEM is then .4898/22.36 = .0219
    4. The margin of error is the SEM * critical value = .0219*1.96 = .0429
    5. The interval is then this margin of error plus/minus the mean or .557 to .643, which we'd say as we can be 95% the true proportion of favorable responses is between 55.7% and 64.3%. You can check these answers using the confidence interval around a proportion calculator.

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