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Question 5 {20 marks] {a} {bl {E} ldl In a survey of 12cc adult men from the Asian ethnicity in Australia it was observed that 45 of them had married to women from Australian ethnicity. i. Find the sample proportion of Asian men who married to Australian women. [I mark} ii. Calculate the sample size required to construct a 95% condence interval for the true proportion of Asian men who married to Australian women where the margin of error is not greater than (LOGS. You may use the sample proportion as an estimate of the true proportion. {3 marks} In a random sample of 3D!) students from a university in regional c'rty and 4m students from a university in major capital city, we observed that respectively 23E! students and 37"5 students obtained fulltimejobsjust within one month of the completion of their degrees. i. Perform a hypothesis test at the 596 level of significance to determine whether there is a difference in the quality of students' educational outcome of the regional city university and the capital city university? {5 marks} ii. State and verify all the assumptions of the hypothesis test used in the previous part i. {2 marks] iii. Using your answers in part i. and part ii., write a brief statistical report [in less than 25f} words] to a non-specialist audience which states the research question, the analytic process followed, and the results and conclusion. {3 marks] Explain clearly the dffference between the Welch's twosample t test and the twosample pooledvariance t test. Under what circumstance{s] is the twosample pooledvariance ttest preferred over the other test? {3 marks] In an Analysis of Variance [AND'v'All when and why do we use the multiple comparisons procedure? {2 marks]