Continuing problem 29, marketing managers at the soft-drink company have asked their market research consultant to explore further the difference between the proportions of women and men who prefer drinking their brand over the leading competitor. Specifically, the company’s managers would like to know whether the difference between the proportions of female and male consumers who favor their brand varies by the age of the consumers. Use the same data as in problem 29 to assess whether estimates of this difference vary across the four given age categories: under 20, between 20 and 40, between 40 and 60, and over 60. Use a 95% confidence level for each of the four required confidence intervals. Summarize your findings. What recommendations would you make to the marketing managers in light of your findings?