After years of rapid growth, illegal immigration into the United States has decl
ID: 3180116 • Letter: A
Question
After years of rapid growth, illegal immigration into the United States has declined, perhaps owing to the recession and increased border enforcement by the United States (Los Angeles Times, September 1, 2010). While its share has declined, California still accounts for 21% of the nation’s estimated 12.5 million undocumented immigrants. Use Table 1.
In a sample of 40 illegal immigrants, what is the probability that more than 18% live in California? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)
In a sample of 220 illegal immigrants, what is the probability that more than 18% live in California? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)
Comment on the reason for the difference between the computed probabilities in parts a and b.
After years of rapid growth, illegal immigration into the United States has declined, perhaps owing to the recession and increased border enforcement by the United States (Los Angeles Times, September 1, 2010). While its share has declined, California still accounts for 21% of the nation’s estimated 12.5 million undocumented immigrants. Use Table 1.
Explanation / Answer
a) p=0.21 ; n=40
hence std error =(p(1-p)/n)1/2 =0.0644
phat =0.18
P(P>0.18)=P(Z>(0.18-0.21)/0.0644) =1-P(Z<-0.4658)=1-0.3207=0.6793
b)for 220 sample size; std error =0.0275
P(P>0.18)=1-P(Z<-1.0925)=1-0.1373=0.8627
c)As the sample number increases, the probability of more than 18% also increases, due to the increased z value and decreased standard deviation