-n percent of s randomly selected F are G
-Therefore, about n percent of all F are G, where
n = percent
s = sample size
F = a property defining the general population
G = the property surveyed then:
-46 percent (400 x .46 = 184) of 400 randomly selected usual Mississippi Republican primary voters are people who believe that interracial marriage should be illegal
-Therefore, about 46 percent of all usual Mississippi Republican primary voters are people who believe that interracial marriage should be illegal
Now, the soundness of statistical generalizations is dependent completely upon the randomness of the sampling. According to my book on statistical reasoning,
"A randomly selected sample is chosen by a method guaranteeing that each of the F's has an equal chance of being chosen. If a large sample sample of F's is randomly selected, it is likely (although not certain) that the proportion of G's in the sample approximates the proportion of G's among all F's."
I do this because I'm confident that this poll will have its methodology challenged, given the potential political ramifications of its findings and the statistical inferences that can be derived from it. According to Dustin Ingalls, the Assistant to the Director of Public Policy Polling, "We poll random samples of registered voters, which means they're distributed proportionately across the state." Hence, the random sampling question is settled, given that it is a necessary condition of a respectable statistical generalization. What we can conclude without the assistance of statistical reasoning however is the fact that there are many in Mississippi who should hang their heads in shame.
The PPP poll is especially detrimental to Republicans, many of whom identify as conservatives because, according to a Gallup poll, "Mississippi is home to the largest percentage of conservatives among U.S. states, with a slim majority identifying their political views as conservative."