in 1996, the General Social Survey asked, \"On the whole, do you think it should

Question

in 1996, the General Social Survey asked, "On the whole, do you think it should be the governments responsibility to provide industry with the help that it needs to grow?" For this question, 206 people said that it definitely should out of 1572 randomly selected people. What is the 90% confidence interval for the proportion of all Americans that believe who it is the government's responsibility?

(0.130, 0.176)

(0.117, 0.145)

(0.105, 0.157)

Assumptions are not met. Can not make confidence interval.

Explanation / Answer

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.131043257          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.008510991          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    1.644853627          
Thus,              
Margin of error = z(alpha/2)*sp =    0.013999335          
lower bound = p^ - z(alpha/2) * sp =   0.117043922          
upper bound = p^ + z(alpha/2) * sp =    0.145042592          
              
Thus, the confidence interval is              
              
(   0.117   ,   0.145   ) [ANSWER, B]

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