In order to judge the effectiveness of an advertising campaign for a certain brand of pretzel, a company obtained a simple random sample of 90 convenience store receipts the week before the ad campaign began, and found that 21 of them showed a purchase of the pretzels. Another simple random sample of 70 receipts was taken the week after the ad campaign, and 39 of them showed a pretzel purchase.

a. Construct a 98% confidence interval for the difference between the proportions of customers purchasing pretzels before and after the ad campaign.

b. A marketing manager claims that the proportion of customers who purchased pretzels did not change after the ad campaign.

Does the confidence interval contradict this claim?