Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Practice lab test

Started: Feb 4 at 19:58

Quiz Instructions

Instructions

(These instructions apply for the actual lab test and are included here for reference.)

This test is conducted under examination conditions. You must work by yourself, without discussing the problems with anyone else.

You may use any printed or hand-written materials, or electronic materials stored on your computer.

You may NOT use internet access, other than to access the LMS.

You may NOT use any computer software other than R/RStudio, and a web browser for accessing the LMS.

An electronic version of the data used in this test is available from the LMS (see links below).

Use R/RStudio to do any calculations and visualisations required to answer the questions on this test, and then type your answer in the answer boxes provided.

We highly recommend that you keep a saved local of your answers (which you can copy into the answer boxes), in case you lose access to the internet and/or LMS during the test. A good way to do this is as an R script within RStudio.

Marks will primarily be awarded for correct answers, irrespective of your method and R code used. However, we suggest you also include a very brief description of your method and a copy of your main R commands, which we can use to potentially award partial marks in case you make an error.

Datasets

Questions 1-5 refer to the data in the file ProdAB.txt

(https://canvas.lms.unimelb.edu.au/courses/182885/files/17746935?wrap=1)

(https://canvas.lms.unimelb.edu.au/courses/182885/files/17746935/download?download_frd=1) , which shows the weights of product A (denoted as ProdA ) and product B (denoted as ProdB ). Assume the weight of product A is  and the weight of product B is 

Questions 6-10 refer to the data in the file Apartment.csv

(https://canvas.lms.unimelb.edu.au/courses/182885/files/17746936?wrap=1)

(https://canvas.lms.unimelb.edu.au/courses/182885/files/17746936/download?download_frd=1) , which shows the size (in m ) and the change in price (in thousands of dollars) between 2015 and 2020 of several apartments.

Question 1

(This question refers to the ProdAB.txt data file.)

Report the 5-number summary statistics (minimum, 1st quartile, median, 3rd quartile, maximum) of Product A.

Question 2

(This question refers to the ProdAB.txt data file.)

Calculate a 90% confidence interval for 

Question 3

(This question refers to the ProdAB.txt data file.)

Assume that σA = σB. Using a 5% significance level, test whether μA < μB. Clearly state your hypotheses, the p-value and your conclusion.

Question 4

(This question refers to the ProdAB.txt data file.)

Consider testing H0:μB = 12 versus H1:μB = 15. Let T be the usual t- test statistic. Find a critical region with a 5% significance level.

Question 5

(This question refers to the ProdAB.txt data file.)

Consider testing H0:μA = 10 versus H1:μA ≠ 10. Let be the usual t- test statistic. Suppose the test is of the form 'reject H0 if |T| > 2'. What is the type I error rate?

Question 6

(This question refers to the Apartment.csv data file.)

Give an estimate of the correlation between the size and the price change.

Question 7

(This question refers to the Apartment.csv data file.)

Fit a simple linear regression model that predicts the price change based on the size of the apartment. Use the usual parameterisation, E(Y|X = x) = α + βx. Give point estimates of all three parameters in the model.

Question 8

(This question refers to the Apartment.csv data file.)

Calculate a 90% confidence interval for β.

Question 9

(This question refers to the Apartment.csv data file.)

A real estate agent wants to predict the price change of an 80 m2 apartment. Calculate a 95% prediction interval for the price change.

Question 10

(This question refers to the Apartment.csv data file.)

Calculate a 90% confidence interval for σ2.