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ETF2121/ETF5912 Data Analysis in Business Assignment 2
发布时间：2023-09-28
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ETF2121/ETF5912 Data Analysis in Business
Assignment 2
Submission guidelines:
● The assignment must be submitted through Moodle using the link Assignment 2 Online Submission. No email submission is accepted.
● The assignment must be submitted before October 6th (Friday), 11:30pm (Australian Eastern Standard 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 is an individual assignment.
· Answer the questions directly. Do not undertake tests or discuss matters not germane to the
specific question.
● This assignment is worth 20 marks.
Question A(3 marks)
A computer programmer claims that MacBooks using the Apple M1 chip are slower than
MacBooks using the Intel chip. He wrote 10 programming scripts using R and ran each script on a MacBook witha M1 chip and a MacBook with an Intel chip. The time it took for each MacBook to execute the script is recorded in Excel file A2 macbook.xlsx.
(a)Use the p-value approach to evaluate the computer programmer's claim at the 10% significance level. Write down the five steps of hypothesis testing (you can use appropriate Excel functions to conduct you analysis but do not copy/paste a screenshot of your Excel output). Present your test statistic and p-value rounded to three decimal places.
Question B(4 marks)
A company is interested in how workers respond to wage cuts. The company formed 30 teams, each consisting of two employees, to sell coffee machines. All employees are paid the same daily wage initially. After a short period of time, teams were unknowingly randomly assigned to one of three pay-cut schemes(treatments). In treatment 1, one of the workers in the team receives a 25% pay cut while the other worker receives the same pay as before the treatment. In treatment 2, both workers in the team receive a 25% pay cut. In treatment 3, neither worker receives a pay cut. Excel file A2 sales.xlsx records the change in the number of coffee machines sold per day after the treatment. The company wants to know if the average change in the sales number differed depending on the which pay-cut scheme a team received.
(a)Specify the null and the alternative hypothesis of interest to the company.
(b)Specify the test statistic and its null distribution.
(c)From this data, does the average change in sales number differ depending on which treatment the team received? Use a 1% significance level and the critical value approach for the test. Use appropriate Excel functions to conduct you analysis but do not copy/paste a screenshot of your Excel output. Present your test statistic and critical value rounded to two decimal
places.
Question C(3 marks)
A gym consultant hypothesis that single people go to gym more often than married people. He surveyed 8 single people and 7 married people using the following questionnaire, where a score for each answer are given alongside the answer.
· How often do you go to gym?
|
Less than once a weel, |
1 |
||
|
once |
a week |
|
2 |
|
2～3 |
times a week |
|
3 |
|
4～6 |
times a week |
|
4 |
|
More |
than 6 times |
a week 5 |
|
The answers from the 15 people are recorded in Excel file A2 gym.xlsx. Use the data to answer the following questions.
(a)Do the data support the consultant's hypothesis that single people go to gym more often than married people at the 5% level? Write down the five steps of hypothesis testing (you can use appropriate Excel functions to conduct you analysis but do not copy/paste a screenshot of your Excel output).
Question D(10 marks)
Marketers are interested in how social media (e.g. Facebook and Twitter/X) activity are related to the box office revenues of movies. Researchers collected the opening weekend box office revenue (in millions of dollars) for a sample of 23 recent movies. In addition, researchers obtained the tweet rate of each movie(average number of tweets referring to the movie per hour) in the week prior to the movie's release. The data are recorded in Excel file A2 boxoffice.xlsx. Use EViews to answer the following questions.
(a)Present a scatterplot of the data with the fitted line.
(b)Write down a population simple linear regression model.
(c)Use EViews to estimate the coefficients and write down the point estimate of the intercept and the slope coefficient.
(d)Interpret the intercept and slope estimated.
(e)Test the null hypothesis that there is no relationship between twitter rates and box office revenue
at the 5% significance level?
(f) In a sentence or two explain why the zero conditional mean assumption might not hold for
this model. That is, what other factors impacting box office revenue left in the error term might
be related to tweet rates.
(g)From the OLS estimates, how would the revenue change (on average) if the tweet rate increases
by 50?
(h)It is unlikely that the relationship between box office revenue and tweet rated be linear. An economist suggests that a better approach would be to estimate the elasticity of box office revenues with respect to tweet rates, that is, the percentual increase in revenues that would be expected for a 1% increase in tweet rates. Write down a simple linear regression model in which
the slope parameter βi can be interpreted as the elasticity.
(i) Estimate the new model and interpret the slope coefficient estimate.
(j) Based on the model estimated on the previous item, what is the average percentual increase in revenues for a movie if its tweet rate increases from 50 to 100 per hour? What about for a movie
for which the tweet rate increases from 500 to 550?
