For the following questions determine the following:

Determine if it is an inference problem for one or two proportions.

What are the key words or phrases that imply inference for one or two proportions?

Identify the key context that implies inference for one or two proportions. (One sample or two samples collected)

1. Feder and Dugan (2002) reported a study in which 404 domestic violence defendants were randomly assigned to counseling and probation (the experimental group) or just probation (the control group). Out of 230 people in the counseling group, 55 were arrested within 12 months. Out of 174 people assigned to probation, 42 were arrested within 12 months. Determine whether counseling lowered the arrest rate; use a 0.05 significance level. Start by comparing the percentages.
2. In June 2012, a Gallup Poll asked U.S. adults whether immigration was a good thing or a bad thing for the country. Out of 1004 respondents, 663 said it was a good thing.Find a 95% confidence interval for the proportion who believe immigration is a good thing.
3. A randomized, placebo-controlled study of a diet drug (Meridia) was done on overweight or obese subjects and reported in the New England Journal of Medicine (James et al. 2010). The patients were all 55 years old or older with a high risk of cardiovascular events. Those who had a heart event had either a heart attack, a stroke, or death from heart-related factors.559 out of the 4906 the patients in the treatment group had a heart event and 490 out of the 4408 patients in the control group had a heart event. Find 95% confidence interval for the difference in proportions
4. The percentage of female CEOs in 2013 in Fortune 500 companies was 4%, according to Time Magazine (March 18, 2013).A student claims that the proportion of female CEOs in Fortune 500 companies has changed.Suppose the student conducts a survey of 250 randomly selected large Fortune 500 companies, and 15 of them had women CEOs. Test the student's claim at the significance level of 0.05.
5. Furman et al. (2014) reported on a study of patients with recurring chronic lymphocytic leukemia (CLL). The study was randomized, double-blind, and placebo-controlled. After 12 months, 101 of the 110 patients assigned to the combination treatment of idelalisib (idel) with rituximab (rit) were still alive, and 88 of the 110 patients assigned to placebo with rit were still alive. Perform a hypothesis test to test whether those who take idel have a better chance of surviving than those taking the placebo. Use a level of significance of 0.05.
6. Harris Interactive conducted a poll of American adults in August of 2011 to study the use of online medical information. Of the 1,019 randomly chosen adults, 60% had used the Internet within the past month to obtain medical information. Use the results of this survey to approximate 95% confidence interval estimate for the percentage of all American adults who have used the Internet to obtain medical information in the past month.