The clerk for a county in Texas reports that the proportion of all registered vo

Question

The clerk for a county in Texas reports that the proportion of all registered voters in the county who will vote for the incumbent (that is, the person currently occupying the elected office) in the next election will be 0.55, or 55%, based on historical voter turnout. A survey conducted by a polling company of a random sample of 600 voters from the county resulted in 294 persons saying that they intended to vote for the incumbent. If the county clerk is correct that the true proportion is 0.55, what is the probability that 294 or fewer voters would say they intend to vote for the incumbent? Report your answer to four decimal places. Hint: This question involves the sampling distribution of the sample proportion.

Explanation / Answer

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value = 294/600 =   0.49      
u = mean = p =    0.55      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.020310096      
          
Thus,          
          
z = (x - u) / s =    -2.954195784      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -2.954195784   ) =    0.001567425 [ANSWER]

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