Use the given degree of confidence and sample data to construct a confidence int

Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

A survey of 400 union members in New York State reveals that 112 favor the Republican candidate for governor. Construct the 98% confidence interval for the true population proportion of all New York State union members who favor the Republican candidate.

0.236 < p < 0.324

0.228 < p < 0.332

0.308 < p < 0.438

0.222 < p < 0.340

0.236 < p < 0.324

0.228 < p < 0.332

0.308 < p < 0.438

0.222 < p < 0.340

Explanation / Answer

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.28          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.022449944          
              
Now, for the critical z,              
alpha/2 =   0.01          
Thus, z(alpha/2) =    2.326347874          
Thus,              
Margin of error = z(alpha/2)*sp =    0.05222638          
lower bound = p^ - z(alpha/2) * sp =   0.22777362          
upper bound = p^ + z(alpha/2) * sp =    0.33222638          
              
Thus, the confidence interval is              
              
(   0.228   ,   0.332   ) [ANSWER, B]

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.