QBM100 Business Statistics\ Session 202390\ Assessment Item 3\ Probability and Inference\ Due date: 28 January 2024\ Value: 20 %\ Task\ This assignment will require you to answer three questions relating to business scenarios that\ will assess your understanding of the content in Topics 6-10.\ Rationale\ This assessment task will assess your progress toward achieving the following learning\ outcomes:\ be able to discuss the basic concepts relating to data analytics (including big data)\ be able to recognise the various types and sources of data\ be able to extract value from data sets for informed decision making;\ be able to identify and determine the appropriate statistical technique to analyse data;\ be able to apply industry software tools to summarise and analyse data;\ be able to present and communicate relevant decisions arising from the analysis of\ data.\ Presentation\ The assignment may be typed or neatly handwritten with any Excel output inserted where\ required at the appropriate place in the assignment not in an Appendix at the back of the\ assignment. Marks will be deducted for assignments which do not follow these guidelines.\ The assignment is to be uploaded to EASTS as a single Word or PDF file. Assignments\ submitted in non-printable formats such as a ZIP file or as a collection of images will not be\ marked. If your scanner produces separate graphics files please paste them into a Word\ document before submitting to EASTS. Pages must be numbered, and your name and student\ number must be included on every page.\ Please view your uploaded assignment in EASTS to ensure all pages, graphs, images, etc\ have uploaded correctly prior to the due date. If you are not able to open your file in\ EASTS then neither will the marker. Assignments that cannot be opened by the marker\ and have to be resubmitted after the due date are likely to be penalised for late submission.\ Marking Criteria:\ Please read each question carefully and be sure to answer the question that is asked. Marks\ cannot be awarded for responses that do not answer the question.\ The grade that you receive for this assignment as a whole is determined by the cumulative\ marks gained according to the tables below (FL 0-49%; PS 50-64%; CR 65-74%; DI 75-84%;\ HD 85-100%).\ Question 1: (15 marks)\ In recent years, several telecommunication companies have been formed that offer competition\ to Telstra in international call costs for residential customers. One of these leading competitors\ advertise that their rates will result in a lower monthly international call bill for residential\ customers than with Telstra. In response, Telstra approached a statistical analyst to conduct\ their own research on the issue, with the hope of forming an argument that there will be no\ difference in customer costs. The research found that the mean monthly bill (international\ calls) for all Telstras residential customers is $24.99. The analyst also took a random sample\ of 100 residential Telstra customers and recalculated their last months bill using the\ competitors rates. This resulted in a mean international call bill of $23.79, with a standard\ deviation of $3.54. Can we conclude, at the 1% significance level, that there is a difference\ between Telstras monthly bills (international calls) for residential customers and those of the\ leading competitor?\ a) State the null and alternative hypothesis. (1 mark)\ b) State the rejection rule/criterion. (1 mark)\ c) Use the Excel (Hypothesis Testing) macro to test the hypothesis. Provide a screenshot\ of your Excel output and state the p-value. (4 marks)\ d) State the outcome of your test. Write a conclusion in the context of the problem. (2\ marks)\ e) The validity of this hypothesis test rests on the sample mean being normally\ distributed. Say how this requirement is satisfied in this situation. (1 mark)\ f) Use the Excel (Estimators) macro to calculate a 99% confidence interval for the\ average monthly international call charges for Telstra customers under the\ competitors rates. Interpret this interval and show your Excel output. (4 marks)\ g) Explain how your confidence interval is consistent with your conclusion from the\ hypothesis test in part (d). (2 marks)\ Question 2 (25 marks)\ a) A company which manufactures microwaves advertises that 90% of their microwaves\ are flawless, requiring no adjustments. Their quality control department tests this\ percentage on a regular basis. On one such test, a random sample of 15 microwaves\ were selected and tested for overall quality. Let X denote the number of flawless\ microwaves.\ i) State the distribution of X and give the value(s) of its parameter(s). (2 marks)\ ii) Calculate the expected number of flawless microwaves. (1 mark)\ iii) Calculate the probability that in this sample, at least 12 microwaves are\ flawless. Show logical working, the Excel function, Excel output and\ interpret your answer. (4 marks)\ A large order of 100 microwaves is filled by randomly selecting from warehouse\ stock.\ iv) What is the\