A June 2012 Rasmussen Poll showed that 65% of its randomly selected U.S. adults were opposed to banning super-size sugary soft drinks, with a margin of error of 3 percentage points and a 95% confidence interval. Assume the conditions hold.
a. Report the confidence interval for the population percentage that opposed banning super-size sugary soft drinks in 2012, using a carefully worded sentence.
b. If the sample size were larger and the sample proportion stayed the same, would the interval be wider or narrower than the one obtained in part a?
c. If the confidence level were 99% instead of 95%, and nothing else were changed, would the interval be wider or narrower than the one obtained in part a?
d. The total adult population of the United States in 2012 was about 240 million. Suppose the population had been half that. Would this have changed any of your answers?