Fifty-five voters from a sample of 80 indicated that they favored casino gambling in their city. The city council is interested in finding out whether or not there is a significant difference between the proportions of those favoring and not favoring casino gambling in their community. σ in this scenario is ______.
A) 8.94
B) 3.42
C) 4.47
D) 7.42

Question

Quizplus · Accepted Answer

σ (pronounced "sigma") represents the standard deviation of a population. However, in this scenario, we don't have the standard deviation of the population. Instead, we can use the formula for the standard error of the proportion:

σp = sqrt[p(1-p)/n]

where p is the proportion of voters who favor casino gambling, and n is the sample size.

p = 55/80 = 0.6875

σp = sqrt[0.6875(1-0.6875)/80] = 0.056

Therefore, σp (the standard error of the proportion) is approximately 0.056. None of the answer choices match this value exactly, but 0.056 is closest to 0.047 (answer choice C).

Fifty-Five Voters from a Sample of 80 Indicated That They