ETF2121/ETF5912 Data Analysis in Business Assignment 1 Submission guidelines: • The assignment must be submitted through Moodle using the link Assignment 1 Online Submission. No email submission is accepted. • The assignment must be submitted beforeApr 16th (Friday), 11:30pm (Australian East- ern Daylight Time). Please take into account possible internet disruptions and leave ample time to upload your document. You can submit your assignment early if you wish. • You are allowed to upload one document with maximum size 100MB. You can either type down your answers in one Word document, or take photos of handwritten answers then convert them to one PDF document. Your work must be clear and legible. If it cannot be read, or read only with difficulty, your assignment will be returned to you unmarked and you will receive a zero mark for this assignment. • I recommend using apps such as Camscanner (available on both iPhones and Android smart phones) to converts photos of your handwritten answer into the PDF document. This app lets you take a photo then crop and stretch the page so it is aligned and easy to read. The app will also combine multiple pages into one PDF document. Assignment guidelines: • This assignment covers topics from lecture 1 to 4 and tutorials 1 to 4. • This is an individual assignment. • Answer the questions directly. Do not undertake inappropriate tests or discuss irrelevant matters. • This assignment is worth 15 marks. 1 Question A: True or False (3 marks) Directions: Read the background and the statement for each question below carefully. Write down if you think the statement is true or false, and briefly explain why. 1. Background: a nationwide survey on shopping habits intends to obtain stratified samples using age range as the variable for stratification. Statement: the stratified samples can be considered a good representation of the population if shopping habits are similar within each age group and heterogeneous between different age groups. 2. Background: a zoologist is interested in the average weight of an adult wallaby. She sampled the weights of 100 randomly selected adult wallabies and obtained the 95% confidence interval for the population mean of the weight. Statement: if the zoologist sampled the weights of 10000 randomly selected adult wallabies, the 95% confidence interval for population mean is likely to be wider than the 95% confidence interval obtained from 100 wallabies. Question B (3 marks) Suppose you want to conduct a survey of benefit packages available in private businesses in greater Melbourne. You have a directory of businesses that lists companies alphabetically. The directory lists the name of the business, suburb, and number of employees of 2500 businesses. The businesses are equally distributed across 250 suburbs; each suburb has 10 listed businesses. Among the 2500 listed businesses, 200 have less or equal to 10 employees, 350 have 11-25 employees, 550 have 26-50 employees, 950 have 51-100 employee, and 450 have more than 100 employee. A snapshot of a section of the directory looks as follows. 2 Company Name Suburb Number of Employees 2020 Global Business Melbourne less or equal to 10 Abbott Business Port Melbourne 11-25 ABC Business Hawthorn more than 100 Ace Business Carlton less or equal to 10 Active Business St Kilda 51-100 Ada Business South Yarra 26-50 Advantage Business Southbank more than 100 Ahrens Business St Kilda 11-25 All Business South Yarra less or equal to 10 Accredited Business Sydney 26-50 Atkins & Race Business Docklands 26-50 Baker Farlow Business St Kilda more than 100 Betta Business South Yarra 51-100 Better Business Richmond 26-50 1. Describe how to use stratified sampling to obtain a sample of 50. Specify which variable (suburb or number of employee) you would choose for stratification and why you choose this variable, compute the number of businesses you should select from each stratum using propor- tional sampling, and discuss how to obtain the sample. 2. Describe how to use cluster sampling to obtain a sample of 50. Specify which variable (suburb or number of employee) you would choose to form clusters, why you choose this variable, and how to obtain a sample of 50 using single stage sampling. Question C (3 marks) A consumer’s organization is interested in determining the amount of variability in the price of one brand of camera. A survey of 25 retail outlets produces a mean and standard deviation of $380 and $20 respectively. 1. Compute the point estimate of the variance and the 95% confidence interval of the variance in the price of this brand of camera. Report your result (round to two decimal places). 2. What assumption did you have to make to obtain the confidence interval? 3 Question D (6 marks) E-grocers are companies that sell groceries online. An e-grocer company analyzed the market and determined that to be profitable the average order needs to exceed $80. To determine whether or not to expand their service to Melbourne, the company offered trial service in Melbourne and recorded the size of the orders (in $) for a random sample of 85 customers. The data in A1.xlsx records the 85 orders. 1. The company would like to use hypothesis testing to decide whether or not to expand their service to Melbourne. They will expand their service only if it is profitable (i.e. if the the average order is larger than $80). Write down the null and alternative hypothesis for an appropriate test. 2. Interpret type 1 and type 2 error for the test in question 1. 3. Let µ denote the true average order size in Melbourne. Manage A thinks that if µ is smaller than or equal to $80 but the company expanded their service, they would incur a loss of $67,000. Manage B thinks that they would incur a loss of 25,000 if this happens. Which manage would choose a smaller significance level for the test in question 1? 4. We consider the sample size of 85 as large sample. Conduct the test in question 1 at the 1% significance level using the critical value approach. 5. Create a histogram and comment on the shape of the histogram. Does the histogram impact the inference derived in the last question? Explain. 4

































































































学霸联盟