After years of rapid growth illegal immigration into the United States has decli
ID: 3181549 • 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 20% of the nation's estimated 12.3 million undocumented immigrants. Use Table 1. a. In a sample of 40 illegal immigrants, what is the probability that more than 15% live in California? (Round "z" value to 2 decimal places, and final answer to 4 decimal places.) Probability b. In a sample of 240 illegal immigrants, what is the probability that more than 15% live in California? (Round "z" value to 2 decimal places, and final answer to 4 decimal places.) Probability 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 15% also increases, due to the increased z value and decreased standard error. As the sample number increases, the probability of more than 15% also increases, due to the increased Z value and increased standard error.Explanation / Answer
a. Here we need to find P(p>0.15) as this is proportion distribution let us convert p to z
z=p^-p/sqrt(p(1-p)/n)=-0.79
So P(p>0.15)=P(z>-0.79)=0.5-P(0<z<0.79)=0.5+0.2852=0.7852
b. Here z=0.15-0.20/sqrt(0.20*0.80/240))=-1.94
So P(p>0.15)=P(z>-1.94)=0.5-P(0<z-1.94)=0.5+0.4738=0.9738
c. As the sample number increases, the probability of more than 15% also increases, due to increased z value and increased standard error.