4. [10 marks] Energy drinks have become widely popular among adolescents and are also consumed by athletes, particularly those who have just begun their sporting career. A recent paper presented a study on the consumption of energy drinks by teenagers engaged in sports, including quantity consumed and factors that might be associated with consumption. A total of 707 students, selected randomly from sports classes at various schools, completed a questionnaire on energy drink consumption. The following table shows the crosstabulation of regular energy drink consumption by gender: Energy Drinks Gender Yes No Female 192 90 Male 296 129 (a) Assuming this sample is representative of all teenagers engaged in sports, give a 95% confidence interval for the true difference in the proportions of females and males who consume energy drinks. What does the interval say about the difference in energy drink consumption between genders? [4 marks] (b) Another factor recorded on the questionnaire was the frequency of practising sports. The following table gives the summary of results for the 681 students who indicated they practised at least once a week: Energy Drinks Practising Sports Yes No Daily 328 146 2-3 times per week 28 13 Once per week 114 52 Based on this table, is there evidence of an association between energy drink consumption and frequency of practising sports? [6 marks] 4. [10 marks] Energy drinks have become widely popular among adolescents and are also consumed by athletes, particularly those who have just begun their sporting career. A recent paper presented a study on the consumption of energy drinks by teenagers engaged in sports, including quantity consumed and factors that might be associated with consumption. A total of 707 students, selected randomly from sports classes at various schools, completed a questionnaire on energy drink consumption. The following table shows the crosstabulation of regular energy drink consumption by gender: Energy Drinks Gender Yes No Female 192 90 Male 296 129 (a) Assuming this sample is representative of all teenagers engaged in sports, give a 95% confidence interval for the true difference in the proportions of females and males who consume energy drinks. What does the interval say about the difference in energy drink consumption between genders? [4 marks] (b) Another factor recorded on the questionnaire was the frequency of practising sports. The following table gives the summary of results for the 681 students who indicated they practised at least once a week: Energy Drinks Practising Sports Yes No Daily 328 146 2-3 times per week 28 13 Once per week 114 52 Based on this table, is there evidence of an association between energy drink consumption and frequency of practising sports? [6 marks]