Exercise 2. A beer industry association conducts a survey to determine the preference of beer drinkers for light, regular, and dark beers. A sample of 200 beer drinkers is taken with each person in the sample asked to indicate a preference for one of the three types of beers: light, regular, or dark. At the end of the survey questionnaire, the respondent is asked to provide information on a variety of demographics including gender: male or female. A research question of interest is whether preference for the three types of beer is independent of the gender of the beer drinker. If beer drinkers' preferences depend on their gender, then beer manufacturers could use this information to customize its promotions and advertising for the different target markets of beer drinkers. A. Construct a two-way contingency table (crosstabulation) with beer preferences (light, regular and dark) and gender (male and female) to summarize the data. Preference * Gender Crosstabulation Gender Female Male Total Preference Dark Count 8 25 33 % within Preference 24.2% 75.8% 100.0% % within Gender 11.8% 18.9% 16.5% % of Total 4.0% 12.5% 16.5% Light Count 39 51 90 % within Preference 43.3% 56.7% 100.0% % within Gender 57.4% 38.6% 45.0% % of Total 19.5% 25.5% 45.0% Regular Count 21 % within Preference 27.3% 56 72.7% 77 100.0% % within Gender 30.9% 42.4% 38.5% Total % of Total Count 10.5% 28.0% 38.5% 68 % within Preference 34.0% 132 66.0% 200 100.0% % within Gender % of Total 100.0% 100.0% 100.0% 34.0% 66.0% 100.0% C. Construct another two-way contingency table (crosstabulation) and find the expected frequency for each cell. Preference *Gender Crosstabulation Gender Female Male Total Preference Dark Expected Count % within Preference 11.2 24.2% 75.8% 21.8 33.0 100.0% % within Gender 11.8% 18.9% 16.5% % of Total 4.0% 12.5% 16.5% Light Expected Count 30.6 59.4 90.0 % within Preference 43.3% 56.7% 100.0% % within Gender 57.4% 38.6% 45.0% % of Total 19.5% 25.5% 45.0% Regular Expected Count 26.2 50.8 77.0 % within Preference 27.3% 72.7% 100.0% % within Gender 30.9% 42.4% 38.5% % of Total 10.5% 28.0% 38.5% Total Expected Count 68.0 132.0 200.0 % within Preference 34.0% % within Gender % of Total 100.0% 66.0% 100.0% 100.0% 100.0% 34.0% 66.0% 100.0% D. Check whether each expected frequency is at least 5. E. State Ho and Ha - HO- F. At the 5% significance level, perform a hypothesis test to determine whether beer drinkers" preferences depend on their gender. B. Use the contingency table (crosstabulation) constructed in Part A, construct a bar graph that shows the relationship between beer preferences and gender. Discuss whether there is dependence exists between beer preferences and gender. Count 60 50 40 30 20 10 10 Bar Chart Female Male Gender Preference Dark Light Regular