In a June 2019 Reuters poll based on a representative sample of 400 American independent voters, 65% responded they support samesex marriages. Now suppose we test the null hypothesis π = 0.50 vs. the alternative hypothesis π ≠ 0.50. 

a. Describe (in words) what the symbol π represents here. 

b. Use the One Proportion applet to determine the (approximate) two-sided p-value. 

c. Based on the two-sided p-value you reported in part (b), does 0.50 appear to be a plausible value for π? Explain your reasoning. 

d. Use the One Proportion applet, repeatedly testing other possible values for π, to determine plausible values and construct a 95% confidence interval for π. 

e. Interpret the 95% confidence interval you reported in part (d).