The manager of a grocery store wants to investigate whether offering the chance to win a cash prize will encourage customers to complete the survey that is printed at the bottom of the purchase receipt. To do so, he recruits 500 volunteers. Each volunteer is asked to select a gift card at random from a large bag of gift cards, all of which have the same value. Half of the gift cards are programmed to trigger printing a receipt that includes a survey at the bottom of the receipt along with the promise that completing the survey will register the customer to win $2,000. The other half of the gift cards are
programmed to trigger printing a standard receipt that includes a survey at the bottom, but no offer of a potential reward. Of the 250 volunteers who received the survey with the contest offer, 15 completed the survey. Of the 250 volunteers who received the survey without the contest offer, 10 completed the survey.
Construct and interpret a 96% confidence interval for the difference in the proportions of all customers like these who would complete the survey when receiving a receipt with the contest offer versus those who receive a receipt without the contest offer
