Qbus5001 2015 semester 2 final examination 10 of 17

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QBUS5001 (2015 Semester 2) – Final Examination - 10 of 17 - Question 2 (20 Marks) (a) [6 marks] A piece of research reveals that more than twenty-five percent of the university students in Sydney use an iPhone. A QBUS5001 student would like to verify the result of the research. She takes a random sample of 500 students from the University of Sydney and she finds that 142 students use an iPhone. (i) [5 marks] Perform a complete statistical test at the 5% level of significance using either the rejection region approach or the p -value approach. What conclusion will the student draw? Note: If you use the p -value approach, the p -value must be calculated using Excel. (ii) [1 mark] State the required conditions for the validity of the statistical test in (i). Are these conditions satisfied? (b) [8 marks] A financial institution requires its new employees to attend a new training course three months after they join the company. This is a training course to improve employee’s understanding of the company’s mission, values, directions, operations, and clients, etc. Before attending this training course, the Human Resources Manager asks each new employee to complete a questionnaire and a score, X , is obtained. After attending the training course, the employee will complete a different questionnaire and another score, Y , is obtained. The Human Resources Manager takes a random sample of 80 new employees and their scores are obtained and are given in Spreadsheet "Q2(b)". Let X and Y be the population means of X and Y . Instruction: Go to Spreadsheet " Q2(b) " . Perform suitable statistical tests using the p-value approach and answer the following questions. The value of the test statistic and the p-value must be given in your answers. Use α = 0.05 in all tests. (i) [3 marks] Test, using a nonparametric method, whether or not this training course can change an employee’s understanding of the company’s mission, values, directions, operations, and clients, etc. (ii) [4 marks] The developer of this training course claims that this course can help increase the score by more than 10 points. Use a parametric test to test the
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QBUS5001 (2015 Semester 2) – Final Examination - 11 of 17 - hypothesis. What assumption(s) do you need to make in order to have a valid conclusion? (iii) [1 mark] If α = 0.01 is used in (ii), what conclusion will you draw? (c) [6 marks] The daily percentage returns of the Insurance Australia Group (IAG) share price and the Suncorp Group (SUN) share price in 2014 are obtained and are saved in Spreadsheet "Q2(c)". Let X and Y denote daily percentage returns of IAG and SUN share prices. Assume that 2 , ~ X X N X , 2 , ~ Y Y N Y and X and Y are independent.
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