A July 2011 Roper Poll showed that 59% of its randomly selected U.S. adults would support banning smoking in all public places. (This was up from 44% in July 2010.) Suppose the margin of error was 4 percentage points with a 95% confidence interval. Assume the conditions hold for all parts.
a. Report the confidence interval for the population percentage that sup-ported banning smoking in all public places in 2011, using a carefully worded sentence.
b. If the sample size were smaller 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 90% and nothing else changed, would the interval be wider or narrower than the one obtained in part a?
d. The total population of adults in the United States in 2011 was about 238 million. Suppose the population had been about one-quarter of that. Would that have changed any of your answers?