In 2015, Company X had 50% of the domestic beer market, Company Y had 30%, and Company Z had 20%. Since then, the three companies have introduced new products and have doubled their advertising expenditures. Three random samples of 500 beer consumers each were selected last month, and the results are as follows: Sample 1: 300 of the 500 consumers chose Company X beer Sample 2: 120 of the 500 consumers chose Company Y beer Sample 3: 80 of the 500 consumers chose Company Z beer (a) Construct a 95% confidence interval for the difference between the proportions of all Company X beer consumers and all Company Y beer consumers. (b) Has the market share of each company changed since 2015? Use a significance level of 1%.

ROUND ALL YOUR ANSWERS TO THE FOURTH DECIMAL PLACE.