During a period of 11 years 674 of the people selected for g

During a period of 11 years 674 of the people selected for grand jury duty were sampled, and

69% of them were immigrants. Use the sample data to construct a 99% confidence interval estimate of the proportion of grand jury members who were immigrants. Given that among the people eligible for jury duty 68.9% of them were immigrants, does it appear that the jury selection process was somehow biased against immigrants?

_ < p < _

Solution

a)

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] =    0.017814574          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.33          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.648492042          
upper bound = p^ + z(alpha/2) * sp =    0.731507958          
              
Thus, the confidence interval is              
              
(   0.648492042   ,   0.731507958   ) [ANSWER]

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As 0.689 is inside this interval, then NO, it doesn\'t appear that the jury selection process was somehow biased against immigrants.