A company that has many department stores in the southern states wanted to find at two such stores the percentage of sales for which at least one of the items was returned. A sample of 800 sales randomly selected from Store A showed that for 280 of them at least one item was returned. Another sample of 900 sales randomly selected from Store B showed that for 279 of them at least one item was returned.
a. Construct a 98% confidence interval for the difference between the proportions of all sales at the two stores for which at least one item is returned.
b. Using a 1% significance level, can you conclude that the proportions of all sales for which at least one item is returned is higher for Store A than for Store B?