Question

During the 2004 senatorial campaign in a large southwestern state, illegal immigration was a major issue. One of the candidates argued that illegal immigrants made use of educational and social services without having to pay property taxes. The other candidate pointed out that the cost of new homes in their state was 20–30% less than the national average due to the low wages received by the large number of illegal immigrants working on new home construction. A random sample of 5,500 registered voters was asked the question, "Are illegal immigrants generally a benefit or a liability to the state’s economy?" The results were as follows: 3,500 people responded "liability," 1,500 people responded "benefit," and 500 people responded "uncertain."

a. What is the population of interest?
b. What is the population from which the sample was selected?
c. Does the sample adequately represent the population?
d. If a second random sample of 5,000 registered voters was selected, would the results be nearly the same as the results obtained from the initial sample of 5,000 voters? Explain your answer.

Answer 1

a

The population of interest is the registered voters , this is because it is the population from which the sample size is selected from.

b

The population is the registered voters of the large southwestern state

c

Well this does not adequately represent the population because this sample where selected from only the registered voters of the large southwestern state and not the whole country

d

Yes the result will be nearly the same because

1. Both samples are selected from the same population
2. The size of the sample selected is sufficiently large to approximate the population

Explanation:

From the question we are told that

The sample size is n = 5,500

Considering question a

What is the population of interest

The population of interest is the registered voters , this is because it is the population from which the sample size is selected from.

Considering question b

What is the population from which the sample was selected

The population is the registered voters of the large southwestern state

Considering question c

Does the sample adequately represent the population

Well this does not adequately represent the population because this sample where selected from only the registered voters of the large southwestern state and not the whole country

Considering question d

Yes the result will be nearly the same because

1. Both samples are selected from the same population
2. The size of the sample selected is sufficiently large to approximate the population