Confidence interval for population proportion given two meansI am trying to estimate a confidence interval containing the true number of people who would vote for Trump. So far, I have calculated the mean number of men who would vote for Trump and the mean number of women who would vote for Trump. I have also rejected the null hypothesis that the means are equal.How would I go about constructing a 95%-confidence interval for the true number of people (men and women) who would vote for him GIVEN my estimates and rejection of equality between the means?

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Charlie Haley · Accepted Answer

Step 1Since you want a 95% confidence interval for the proportion that favors Trump (for men and women), and NOT the difference between men and women who favor trump, then you can do this in a couple ways. One way being by hand or one way using computer software R. I will use the method by hand first. At the end I supply you with code for R.Lets say of 200 men, 100 favor trump and of 100 women, 40 favor trump.Thus, the proportions of men and women who favor trump isp1=.50p2=.40We known1=200n2=100Now we need to compute the Standard Error (SE)SE=p(1−p)nThus, SE1=.035355SE2=.0489898Step 2Now we need to find the Z-Value for a 95% confidence interval, which isZ=1.96We can now compute the Margin of Error(ME) by using the formula Z⋅SEThus, ME1=1.96⋅.0353553=.0692964ME2=1.96⋅.0489898=.09602Step 3Now we can compute the 95% Confidence Interval (CI) for the proportions of men and women who favor Trump, using p1 and p2, and ME1 and ME2Thus, CI1=(.431,.569)CI2=(.304,.496)Alternatively computer software can do this much faster for youprop.test(100,200,conf.level = .95, correct = TRUE)0.4313609,0.5686391prop.test(40,100,conf.level = .95, correct = TRUE)0.3047801,0.5029964

Confidence interval for population proportion given two means I

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