Context: Example 4.4.7

Now to the numbers! Let's begin with Candidate A. We have the following numbers: sample size n = 1350, favorable voters k = 648. Therefore p = 648/1350 = 0.48 or 48%, and p (sqrt 1350 0.48 (1 0.48)) 18.3565, so the standard error is st.err. 18.3565/1350 0.0136 or 1.36%.

This tells us that the percentage of support for Candidate A the day of the poll was between 48 2 1.36 and 48 + 2 1.36, that is between 45.28% and 50.72%.

Similarly, for Candidate B we have n = 1350, favorable voters k = 702. Therefore p = 702/1350 = 0.52 or 52%, and (sqrt 1350 0.52 (1 0.52)) 18.3565, so the standard error is st.err. 18.3565/1350 0.0136 or 1.36%. This tells us that the percentage of support for Candidate B the day of the poll was between 52 2 1.36 and 52 + 2 1.36, that is between 49.28% and 54.72%. When we plot these two intervals one on top the other we clearly see that they overlap.

Question: Show that in Example 4.4.7, page 153, the difference between the two candidates is statistically significant even at a confidence level of 99.7%.