In a July 2012 Gallup poll based on a representative sample of 1014 adult Americans, 48% reported drinking at least one glass of soda pop on a typical day. Now suppose that we test the null hypothesis π = 0.50 vs. the alternative hypothesis π ≠ 0.50.
a. Describe (in words) what the symbol πrepresents 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. How would this two-sided p-value compare to a one sided p-value: larger, smaller, or the same?
e. Use the One Proportion applet for a single proportion, repeatedly testing other possible values for π, to determine plausible values and construct a 95% confidence interval for π.
f. Interpret the 95% confidence interval you reported in part (e).