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Question 2 (20 marks) Cathy is conducting a research on esports. She wants to know the gender distribution of gamers and the number of hours a gamer spends on practising per day. Cathy visited many online esports forum. Overall, she met 33 female gamers and 117 male gamers. She has detailed chat with a random sample of 27 gamers. Among these 27 gamers, she found that the mean practising time per day is 6.04 hours with standard deviation 2.1 hours. (a) Test, at the 5% level of significance, is there sufficient evidence to say that population mean practising time is over 5.5 hours per day? (b) Is there sufficient evidence to conclude that the population proportion of female gamers is less than 0.25? Test the hypothesis at 2% level of significance. (Each test report must include (i) null hypothesis and alternative hypothesis, (ii) rejection region, (iii) calculation of test-statistics, and (iv) conclusion.)