Question 4 ['21 marks} There is an ongoing trade tension between lChina and Australia. In recent months... China has implemented a range of policies that reduces Australian exports to China. An economist predicts that the current trade tension will continue and even get worse in 2MB. In early June, l Australians were surveyed. and ?'55 of them said that the economist's prediction seems reasonable. a} lEalculate the sample proportion of Australians who agree with the economist's prediction. [1 mark] b} Using the sample proportion1 calculate the sample size needed to construct a 95% con- dence interval for a similar survey so that the margin of error is not greater than 0.03. [3 marks] c} lEoncluct a hypothesis test to determine if the true proportion of Australians agreeing with the economist's prediction is more than 0.31.] at the 5% level of signicance. [Ei marks] d} The following table shone the gender specic sample gures of 1,500 Australians. Female Number of Respondents agreeing with the economist's prediction dill] Total Number of Respondents 529 {i} Denote by pm and p; the true proportions of male and female Australians agreeing with the economist. Calculate the sample proportions 15,.\" and gay. [2 marks] {ii} Conduct a hypothesis test to determine if the true proportions of Australians sup- porting the economist is the same among male and female individuals at the 5% level of signicance. [El marks] [iii] State and check all the assumptions for the hypothesis test conducted in part d}|[ii]l. [3 marks]