## Question 507:

Asked on November 12, 2008

Tags:
Sample Size ,
Confidence Intervals ,
Proportion

1

## Answer:

No answer provided yet.

- 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.
- 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.
- The square root of the sample size is SQRT(500) = 22.36
- The SEM is then .4898/22.36 = .0219
- The margin of error is the SEM * critical value = .0219*1.96 = .0429
- 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.