1) Immigration reforms has focused on dividing illegal immigrants into two groups: Long-term and short-term. In a random sample of 1000 construction workers from the Northeast (NE), 70 are illegal short-term immigrants. In the Northwest (NW), 45 out of 1000 are illegal short-term immigrants. Calculate a 90% confidence interval for the difference in proportion of short term immigrants from NE and NW. Note: NE=Sample 1 and NW=Sample 2. Round your answer to 3 decimal places.

Upper Limit =

Lower Limit =

2) As the campaign manager for your local congressional race, you hired Polimetrics, Inc. to conduct a survey to gauge voter support for your candidate. PI conducted a survey involving a random sample of registered voters. The interviewer asked who they would vote for if the election were held today. PI found 47% of the sampled voters support the candidate. You may have noticed that in major national polls, news services report margins of error (half length) around 3%. What sample size is needed in order to retain the 95% confidence level with a half-length of 0.03?

3)Explain why the Central Limit Theorem is important and describe an example.