In a May 2013 Gallup poll based on a representative sample of 1,535 adult Americans, 53% responded that they thought same-sex marriages should be legal and have the same rights as traditional 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 ???? 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 ????? Explain your reasoning.
d. Use the One Proportion applet, repeatedly testing other possible values for ????, to determine plausible values and construct a 95% confidence interval for ????.
e. Interpret the 95% confidence interval you reported in part (d).