RESEARCH SCHOOL OF FINANCE, ACTUARIAL STUDIES AND STATISTICS Quantitative Research Methods STAT1008 Assignment 1 (Total Marks: 40) Due date: 4pm Wednesday 18 Sep 2024 INSTRUCTIONS: • This assignment is worth 10% of your overall grade for this course. • The assignment can be typed or handwritten. It should be completed on your own. Copying someone else’s work or allowing your work to be copied will result in a zero for the assignment and may lead to serious academic consequences. • Your assignment should be submitted to Turnitin as a single pdf or word document including the following: 1. The assignment cover sheet (“Assessment Integrity Declaration" available to down- load from Wattle). 2. Your assignment. • Unless otherwise specified, final numerical solutions should be expressed as four deci- mal places or fractions (e.g. 0.3333 or 1/3). • Include all working, as marks will not be awarded for solutions that do not include working. • Name your assignment “Course code_Uid”, e.g., “STAT1008_u1234567”. • Marks will be deducted if above instructions are not strictly adhered to. • Late submissions will NOT be accepted. Extensions will usually be granted on med- ical or compassionate grounds on production of appropriate evidence, but must have lecturer’s permission at least 24 hours before the deadline. Assignment 1 - Sem 2, 2024 Page 1 of 3 Question 1 [16 Marks] The file “Facebook.xlsx” contains data on posts from a Facebook account. Each row represents a single post and includes the following attributes: • Type: The type of post (e.g., photo, status, video, link). • Paid: A categorial variable indicating whether the post was a paid advertisement (Yes or No). • Lifetime Engaged Users: The number of unique people who engaged with the post (e.g., liked, commented, shared, clicked). • comment: Number of comments on the post. • like: Number of likes on the post. • share: Number of shares of the post. Data Reference: Moro, S., Rita, P., and Vala, B. (2016). Predicting social media performance metrics and evaluation of the impact on brand building: A data mining approach. Journal of Business Research, 69(9), 3341-3351. Based on this dataset, please answer the following questions. (For Excel related ques- tions, only the output is required; you do not need to include the implementation steps.) (a) [2 marks] Create a histogram for the variable “share” and discuss its shape. (b) [5 marks] Generate a summary table of descriptive statistics using the Excel Data Analysis Toolpak, and create a box-and-whisker plot for the variable “Lifetime Engaged Users”. Interpret the results. (c) [5 marks] We want to explore the relationship between “Comment” and “Like” using both numerical measures and graphical tools. Analyse and discuss your findings. (d) [4 marks] Create a two-way contingency table for the variables “Type” and “Paid”. Find the marginal probability that a post is a video. If we know that the post is a paid advertisement, how does this information change the probability that the post is a video? Assignment 1 - Sem 2, 2024 Page 2 of 3 Question 2 [8 Marks] In town, 40% of all households have a pet and 30% of all households have children. For those who have children, 50% have a pet. (a) [4 marks] What is the probability that a randomly selected household has a pet or children? (b) [4 marks] What proportion of households with no pets have children? Question 3 [16 Marks] On its overseas flights, an airline oers three dierent dessert options: ice cream, ap- ple pie, and chocolate cake. Based on historical data, the airline assumes that each dessert has an equal probability of being chosen by a passenger. If a random sample of 50 passengers is selected, approximate the probabilities for the following events by using two methods: (1) normal approximation with continuity correction and (2) CLT. Additionally, use Excel to find the exact probabilities. Finally compare the results. (a) [8 marks] At least 10 passengers will choose ice cream for dessert. (b) [8 marks] Between 12 and 15 passengers (inclusive) will choose ice cream for dessert. Assignment 1 - Sem 2, 2024 Page 3 of 3 51作业君版权所有