-interval for a difference between population proportions

Sure, here are the steps to calculate a confidence interval for a difference between population proportions:

1. Identify a sample statistic: Since we are trying to estimate a population proportion, we choose the sample proportion (p) as the sample statistic.

2. Select a confidence level: In this analysis, the confidence level is defined for us in the problem. We are working with a 95% confidence level.

3. Find the standard deviation or standard error: Since we do not know the standard deviation of the population, we cannot compute the standard deviation of the sample mean. Instead, we compute the standard error (SE). SE for two proportions is calculated as sqrt{ [ P1(1 - P1) / n1 ] + [ P2(1 - P2) / n2 ] } where P1 and P2 are sample proportions and n1 and n2 are the sizes of the samples.

4. Find the margin of error: Elsewhere on this site, we show how to compute the margin of error when the sampling distribution is approximately normal. The key steps are shown below:

   • Find standard deviation or standard error.
   • Multiply by the appropriate z*-value (for the desired confidence level).

5. Specify the confidence interval: The range of the confidence interval is defined by the sample statistic plus the margin of error. The uncertainty is denoted by the confidence level.

Remember, the calculation for the range of a confidence interval is:

Confidence Interval = sample statistic ± (z*-value * standard error)

In this case, the sample statistic is the difference between the two sample proportions (P1 - P2).