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 27% of the nation’s estimated 10.6 million undocumented immigrants. [You may find it useful to reference the z table.]

a. In a sample of 60 illegal immigrants, what is the probability that more than 24% live in California? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

b. In a sample of 210 illegal immigrants, what is the probability that more than 24% live in California? (Round “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 24% also increases, due to the lower z value and decreased standard error.

• As the sample number increases, the probability of more than 24% also increases, due to the lower z value and increased standard error.

Answer 1

p = 0.27

(a) n = 60, P(P>0.24) = 1 - P(P< 0.24)

Therefore P(P<0.24) = 0.2946

Therefore P(P>0.24) = 1 - 0.2946 = 0.7054

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(b) n = 210, P(P>0.24) = 1 - P(P< 0.24)

Therefore P(P<0.24) = 0.1539

Therefore P(P>0.24) = 1 - 0.1539 = 0.8461

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(c) Option 2: As the sample number increases, the probability of more than 24% increases, due to the lower z value and the increased standard error.

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