In a USA Today/Gallup poll survey carried out in 2009, 57% of 1006 randomly sampled American adults said that abortions should be legal only under certain circumstances when asked, "Do you think abortions should be legal under any circumstance, legal only under certain circumstances or illegal in all circumstances?" (Source: https:// www.pollingreport.com/abortion.htm).
a. Calculate a 95% confidence interval that estimates the proportion of all Americans in 2009 who thought abortions should be legal only under certain circumstances.
b. On the basis of this confidence interval, is it reasonable to infer that in 2009 more than half of all Americans thought that abortions should be legal only under certain circumstances? Explain.
c. In the survey, 18% answered that abortions should be illegal in all circumstances. Calculate a 95% confidence interval that estimates the proportion of all Americans in 2009 who thought abortions should be illegal in all circumstances.