After years of rapid growth, illegal immigration into the United States has decl
ID: 3183398 • 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 31% of the nation's estimated 10.8 million undocumented immigrants. Use Table 1. a. In a sample of 40 illegal immigrants, what is the probability that more than 30% live in California? (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) b. In a sample of 280 illegal immigrants, what is the probability that more than 30% live in California? (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) c. Comment on the reason for the difference between the computed probabilities in parts a and b. As the sample number increases, the probability of more than 30% also increases, due to the increased z value and decreased standard deviation As the sample number increases, the probability of more than 30% also increases, due to the increased z value and increased standard deviationExplanation / Answer
p=0.31
std error =(p(1-p)/n)1/2 =0.073
hence P(X>0.30) =1-P(X<0.30)=1-P(Z<(0.3-0.31)/0.073)=1-P(Z<-0.1367)=1-0.4456=0.5544
for n=280
std error =0.0276
P(X>0.30)=1-P(Z<-0.3618)=1-0.3587 =0.6413
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