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STAT7055 Introductory Statistics for Business and Finance

INSTRUCTIONS TO STUDENTS

Due Date

● The assignment is due at 6:00pm on Friday October 22. Note that this is different to the time and date stated in the class summary.

● Late submission of the assignment is not permitted. An assignment submitted without an extension after the due date will receive a mark of 0.

Obtaining your Assignment

● There are different versions of the assignment and each student will be assigned a particular version of the assignment.

● Therefore, you must log in to Wattle with your own ANU credentials and download your assignment directly from Wattle.

Writing your Assignment

● The assignment is an individual piece of assessment and must be completed on your own.

● You will be required to write a report in an R Markdown document that contains R code, R output and written text. An example of an R Markdown document, which you can use as a template, has been provided on Wattle.

● When answering the assignment questions in your report, you will need to include all your R code and R output that you used to calculate any answers and you must also write your answers in proper sentences. For example, if you are required to calculate a sample mean, then you would include your R code and R output for calculating the sample mean and you would also write a proper sentence in the report such as “The sample mean is equal to ...”.

● Make sure to be clear and concise in your answers.

● A good way to approach writing your report is to imagine that you are a statistical consultant and that a client has asked you to do some statistical analyses. When presenting the results of your analyses to the client, you wouldn’t just give them pages of R code or pages of R output. Rather, you should give them a proper report which clearly outlines and explains the results of the analyses and which also includes the R code and R output used to produce the results.

● Once you have finished writing your report in your R Markdown document, you will need to render the document by pressing the Knit button in RStudio to create a HTML file of your report.

● Further to the above point, it is good practice to regularly Knit your R Markdown document as you write your report. This is useful for checking that it’s rendering properly.

Submitting your Assignment

● Submission of the assignment will be through Wattle via Turnitin.

● A Turnitin link with further details regarding assignment submission will be provided on Wattle.

● For submission you will need to submit two files: the R Markdown file of your report (i.e., a “.Rmd” file) and the rendered HTML file of your report produced by pressing the Knit button in RStudio (i.e., a “.html” file).

● Please name your two files as “uNNNNNNN.Rmd” and “uNNNNNNN.html”, where uNNNNNNN is your student number.

● No other file types can be submitted, e.g., “.R”, “.docx”, “.RData”, “.zip”, etc., files will not be accepted. In particular, do not submit any compressed files.

Other Important Details

● You may only use built-in functions available in base R and you are not permitted to use functions in any additional R packages (e.g., ggplot2).

● You must use the appropriate R functions (and not the statistical tables) to calculate critical values or p-values for the normal, t and F distributions.

● Round all final numeric answers to 4 decimal places. However, as you will be using R, keep all decimals during all intermediate steps to ensure the accuracy of your final numeric answer.

● Please use the help function if you want to learn more about a particular R function, e.g., enter help(mean) in the R console to learn more about the mean function.

● For questions that require writing mathematical symbols, you are welcome to use shorthand notation, provided you make the meaning clear (e.g., using “Mu” for µ, or “!=” for ).

● Answers need to be written in the text of the R Markdown document and not in the comments of code chunks.

● Do not print out the entire data sets in your R Markdown document, as this will only take up unnecessary space.

Question 1 [14 marks]

A streaming service provider would like to better understand the weekday viewing habits of their subscribers. In each year from 2015 to 2019, the provider conducted a short survey where they randomly selected 200 subscribers and asked each subscriber the following two questions:

1. The weekday on which they used the streaming service the most.

2. Their age.

Note that each year, a new random sample of subscribers was selected for the survey. The data are stored in the file AssignmentData.RData in the data frame Q1.df. The data frame contains two columns for each year, one for the weekday on which the subscriber used the streaming service the most and one for the subscribers’s age . For example, for the year 2015 there are two columns, Weekday2015 and Age2015.

For parts (a), (b) and (c), you will be analysing data from the 2017 survey.

(a) [4 marks] Create a boxplot and a histogram of the subscribers’ ages for the 2017 survey. Make sure to give each plot a proper descriptive title and label the x-axis of the histogram appropriately (do not just use the default title or labels). Based on these plots, describe the distribution of the subscribers’ ages for the 2017 survey. Be specific in your description, making sure to mention any interesting and/or important aspects of the distribution.

(b) [3 marks] Test whether the population proportion of subscribers in 2017 that are at least 33 years old is less than 0.4. Clearly state your hypotheses, making sure to define any parameters, and use a significance level of α = 1%. Do not use any R functions that are designed to perform hypothesis tests.

(c) [3 marks] Create a bar chart describing the weekdays on which subscribers used the streaming service the most for the 2017 survey. Think carefully about how to appropriately present this data in the bar chart. Make sure to give the bar chart a proper desc