Construct the indicated confidence interval for the difference in proportions. Assume that the samples are independent and that they have been randomly selected. A marketing survey involves product recognition in New York and California. Of 558 New Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product. Construct a 99% confidence interval for the difference in the proportions of New Yorkers and Californians who knew the product. At the 0.05 significance level, do the data provide sufficient evidence to conclude that the recognition rate in New York differs from the recognition rate in california? Construct a 99% confidence interval for the difference between two population proportions. Explain your conclusion .