It is hard to persuade consumers to abandon a product with which they are familiar. One experiment gave consumers free samples of a new laundry detergent and also a standard detergent. After some time, ask the subjects which detergent they prefer. Here are the data.

Prefer new product: 19 User, 31 Non User

Prefer standard product 29 User, 27 Non User

(a) Calculate a 90% confidence interval for the difference in proportions between nonusers and users of the standard detergent that prefer the new detergent.

(b) Based on the confidence interval in (a), can we conclude that a significant difference exists between the proportion of nonusers of the standard detergent who prefer the new detergent and the proportion of users of the standard detergent who prefer the new detergent? Explain.