A company conducted a survey on the launch of two types of health drinks. The first type of healthy drink contains fruit vitamins, minerals, and antioxidants. The second contains vegetable nutrition, potassium, dietary fiber, folate (folic acid), vitamin A, and vitamin C. A random sample of 500 customers was asked to state their preference of the products. Of these, 230 had bought the first type of health drink and 88% of them liked the product. The remaining had chosen the second type and 65% of them loved it.

a. Develop a 99% confidence interval for the difference of population proportion of customers who bought the products and liked them. Would you agree that there is a 20% difference in customers who liked the products they bought?

b. Conduct a hypothesis testing at a 1% significance level to test whether there is a significant difference between the two population proportions of customers who bought the products and liked the products.