Suppose a market analyst wants to determine the difference in the average price of a gallon of whole milk in Seattle and Atlanta. To do so, he takes a telephone survey of 21 randomly selected consumers in Seattle who have purchased a gallon of milk and asks how much they paid for it. The analyst undertakes a similar survey in Atlanta with 18 respondents. Assume the population variance for Seattle is 0.03, the population variance for Atlanta is 0.015, and that the price of milk is normally distributed. Using the resulting sample information that follows,

a. Compute a 99% confidence interval to estimate the difference in the mean price of a gallon of milk between the two cities.

b. Using a 1% level of significance, test to determine if there is a significant difference in the price of a gallon of milk between the two cities.