Question

Among registered voters in Michigan, the Democratic candidates range from narrowly ahead to essentially tied with President Trump in head to head election matchups:

Sanders narrowly tops Trump 48 - 43 percent

845 self-identified registered voters in Michigan with a margin of error of +/- 3.4 percentage points

a) Verify the margin of error by doing you own calculation. Include the calculation in your post.
b) Report the confidence intervals for the top two candidates using the most common 95% confidence level. Do they overlap or not?

Answer 1

Answer a)

Formula for Margin of Error is as follows:

ME = +/- z_c*sqrt(p*(1-p)/n)

In this case, p = 0.48, n = 845

The critical value for α = 0.05 is z_c ​= z_1−α/2 ​= 1.96

ME = +/- 1.96*sqrt(0.48*(1-0.48)/845)

ME = +/- 0.034 (+/-3.4 percent points)

Answer b)

95% Confidence Interval Calculation for Sanders

Thus, the 95% confidence intervals for the Sanders is (44.6%, 51.5%)

95% Confidence Interval Calculation for Trump

Thus, the 95% confidence intervals for the Trump is (39.7%, 46.3%)

Thus, we can seen that 95% confidence interval for the top two candidates overlap.