Ipsos surveyed 1005 Canadian adults just after the Black Friday sale in 2014 and found that 24.7% of them had bought something during the Black Friday sales promotions.

a) Calculate a 95% confidence interval for the proportion of Canadian adults buying something during the Black Friday sales promotions in 2014 and interpret its meaning.

b) How many Canadian adults would Ipsos need to survey in order to reduce the width of this confidence interval by 50%?

c) How much wider is the 99% confidence interval than the 95% interval you calculated in (a)? Give your answer as the ratio between the widths of the two confidence intervals.

d) A similar survey by Ipsos of 1010 Canadian adults in 2013 found 27.2% of them had purchased something during the Black Friday sales promotions that year. Calculate a 95% confidence interval for the difference in this proportion between 2013 and 2014 and interpret its meaning. Did the proportion decline between 2013 and 2014?