An advertising agency is judged by the increase in the proportion of people who buy a particular product after the advertising campaign is conducted. In a random sample of 200 people prior to the campaign, 40 said that they prefer the product in question. After the advertising campaign, out of a random sample of 300, 80 say they prefer the product.
(a) Find a 90% confidence interval for the difference in the proportion of people who prefer the stipulated product before and after the advertising campaign.
(b) Can you conclude that the advertising campaign has been successful in increasing the proportion of people who prefer the product? Use a level of significance of 0.10.