ETC2520 - Probability and Statistical Inference for Economics and Business - Econometrics Assignment Help

Assignment Task :

Instructions and Rubric (ETC2520)
The examination paper contains five (5) questions. Candidates are required to attempt all five questions. The questions begin on the following page.
Each question carries a total of 12 marks and the marks for each part of a question are stated in square brackets.
A complete answer-solution to a question should include a clear statement of all the necessary steps in the argument, together with any assumptions and working. Credit
will be given for demonstration of knowledge, thus you should provide a partial answer where you are not able to provide a full one.
Remember that it is your responsibility to demonstrate your understanding of the material, so define any abbreviations you use and provide answers that are clear and
concise.

Question 1.
 

Question 9 

A university administrator believes that only 20% of students enrolled in a Commerce degree will have already decided on a major area of study by the end of the first year of their course. To test the administrator’s belief, a random sample of 160 first-year Commerce students are surveyed, at the end of their second semester of study, and asked if they have in fact already decided on their major. 

(a) Find the form of the uniformly most powerful (UMP) hypothesis test to determine if the belief stated above is true, or if in fact the percentage of all university students enrolled in a Commerce degree will have decided on a major by the end of their first year is greater than 20%. Explain why your test procedure is UMP. 

(b) If 45 of the 160 Commerce students surveyed reported having decided on their major, construct an approximate 95% confidence interval for the percentage outlined in part (a), and state the corresponding test conclusion. Are the confidence interval and test conclusion compatible? – Explain why or why not. 

Question 10 

A real estate agent operating across the eastern suburbs of Melbourne claims that the average selling time of all residential properties in the eastern suburbs of Melbourne is six weeks or 42 days. A sample of 30 recently sold residential properties in the area has a sample average of 49 days and a sample standard deviation of 20 days. 

(a) Undertake a hypothesis test to determine whether the real estate agent’s claim is correct at the 5% level of significance against the alternative that the average selling time of all residential properties in the eastern suburbs of Melbourne is different from six weeks. 

(b) Provide a justification for the sampling distribution of the test you have used to test the null hypothesis in part (a). 

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