In a survey of 500 potential jurors, one study found that 345 were regular watch

Question

In a survey of 500 potential jurors, one study found that 345 were regular watchers of at least one crime-scene forensics television series. (a) Assuming that it is reasonable to regard this sample of 500 potential jurors as representative of potential jurors in the United States, use the given information to construct a 95% confidence interval for the true proportion of potential jurors who regularly watch at least one crime-scene investigation series. (Use Table 3 in Appendix A. Give the answer to three decimal places.) ( 0.731 Incorrect: Your answer is incorrect. , 0.650 Incorrect: Your answer is incorrect. )

Explanation / Answer

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.69          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.020683327          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.96          
Thus,              
Margin of error = z(alpha/2)*sp =    0.04053932          
lower bound = p^ - z(alpha/2) * sp =   0.64946068          
upper bound = p^ + z(alpha/2) * sp =    0.73053932          
              
Thus, the confidence interval is              
              
(   0.64946068   ,   0.73053932   ) [ANSWER]

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