Statistics

  
1 The North American Free Trade Agreement (NAFTA) enacted in 1994 is a trilateral trade agreement signed by the United States, Canada and Mexico. This trade agreement has been controversial since its inception and Americans remain split on the issue. In a Gallup Poll conducted February 1-5, 2017, 470 out of 1022 randomly selected Americans aged 18 or older stated that they believed that NAFTA was bad for the United States.

 
  
a. Find the point estimate for the proportion of Americans who believe that NAFTA was bad for the United States. Round your answer to 4 decimal places.
 
b. Find the margin of error for a 95% confidence interval. Round your answer to 4 decimal places.
 
c. Construct the 95% confidence interval for the proportion of Americans who believe that NAFTA was bad for the United States. Enter your answer as an open interval of the form (a,b) and round to 3 decimal places.
 
d. Can you conclude that more than half of Americans believe that NAFTA was bad for the United States? 
o No conclusions can be drawn since the confidence interval contains 0.50.
o Yes, the entire confidence is above 0.50.
o No, the entire confidence interval is below 0.50.
2 The Affordable Care Act (ACA) signed into law by President Barrack Obama in 2010 was the most significant regulatory reform of the United  States healthcare system since the passage of Medicare and Medicaid in 1965.  The law was designed to expand insurance coverage and reduce the costs of health care.  Some elements of the law such are banning insurance companies from denying coverage to people with pre-existing conditions are popular while other provisions such as the individual mandate are unpopular.  Opinions on the law vary with some wanting to keep the law as it it, others favor fixing the law and some favor repealing the law in its entirity. The middle position has been gaining traction recently and in a Rasmussen Reports poll conducted January 5, 2017, 521 out of 931 randomly selected likely voters want Congress and the President to fix the law a piece at a time.

 
  
a. Find the point estimate for the proportion of Americans who want Congress and the President to fix the law a piece at a time. Round your answer to 4 decimal places.
 

 
b. Find the margin of error for a 95% confidence interval. (ound your answer to 4 decimal places.
 

 
c. Construct the 95% confidence interval for the proportion of Americans who want Congress and the President to fix the law a piece at a time. Enter your answer as an open interval of the form (a,b) and round to 3 decimal places.
 

3 A political candidate has asked you to conduct a poll to determine what percentage of people support her.
 
If the candidate only wants a 6% margin of error at a 90% confidence level, what size of sample is needed?
 
Give your answer in whole people.
4 If n = 320 and ˆpp^ (p-hat) = 0.75, construct a 95% confidence interval.
 
Give your answers to three decimals
5 Out of 600 people sampled, 510 had kids. Based on this, construct a 99% confidence interval for the true population proportion of people with kids.
 
Give your answers as decimals, to three places
 
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