**The Assignment**:

This Assignment is an **individual** based task which requires students to apply principles covered in previous classes to real life situations. You are required to complete both sections of this Assignment and submit your written report within two weeks.

The first section involves data collection and analysis and requires you to demonstrate your knowledge of statistics **explaining** your interpretation and reasoning clearly, taking care that your answers and explanations are **original** and all data collected are **appropriately referenced**.

The second section on MATLAB must be done on a computer using the actual software and original **MATLAB printouts** must be included in your submission.

**The Report:**

Your report should include a cover page with your name, student number, subject name, assessment title, submission date and teacher’s name (this is in addition to the assignment cover sheet that is attached during submission).

Your solution to each problem should include an introduction which outlines the problem in your own words, **your mathematical solution which should be accompanied by written explanations**, and your **conclusions should explain your findings in the context of the problem**.

The MATLAB section of the report must include **original MATLAB****printouts**. This must include printouts of the command Window and the script files for the task. MATLAB commands typed up in Word/Notepad are **not acceptable**. Also ensure that your **name and student number** appear within your code either in the script file or in the command window.

**Assessment Criteria:**

Your project will be assessed according to the criteria sheet provided at the end of this Assignment and will based on:

your interpretation of problems

application of the appropriate concepts taught in your course the logical reasoning and clarity of your explanations steps shown in all your calculations the presentation of the solutions the accuracy of your answers and graphs appropriate interpretation of results/conclusions made.

Take care to show all steps, relating the numbers and units to the context and follow all graphical conventions. Ensure that you address each criterion in your written responses.

**Section I **

This section involves the collection and analysis of data and the use of inferential statistical methods to draw conclusions from the findings. You are required to complete both the tasks in this section clearly explaining your choice of data, the analysis methods used and discussing your findings and conclusions in the context of each task.

The purpose of this task is to analyse seasonal rainfall and any change in rainfall pattern over time.

Go to the following website: __http://reg.bom.gov.au/climate/data/?ref=ftr__

1: Select Data about: RAINFALL

Type of Data: Observations, Monthly.

Choose any town/suburb in any state of Australia and select one of the nearest Bureau stations and select ‘Get data’. A table with your selection opens in a new window.

At the bottom of the table select: “View all monthly data”

If your town or station is less than 50 years old, pick another one that has data for at least 50 years prior to 2003. Choose any month and collect the rainfall data for that month over a time period of at least 50 years earlier than 2003. For example, you may choose data from 1856 to 1910 or from 1950 to 2000.

Choose another month, 6 months away from your previous month. Collect **the same** 50 years of rainfall data for this month.

For each month selected calculate the mean and standard deviation of the rainfall. Construct a 99% confidence interval for the rainfall during each of the months.

Discuss your findings. Explain any unknown variables which may have affected your conclusions.

Now look at the rainfall in the year 2013 for the same two months you selected above. Do these values lie in the respective confidence intervals you constructed? Comment on your findings.

The purpose of this task is to investigate statistically whether there is a significant change in temperature over time.

Go to the same website: __http://reg.bom.gov.au/climate/data/?ref=ftr__

1: Select TEMPERATURE

Type of Data: Observations, Daily, Max Temp.

Choose any city in Australia and select one of the nearest Bureau stations.

Choose a month and collect the temp data for that month for two different years (the selected years should be at least 30 years apart).

You are required to determine whether the average temperature has changed significantly over 30 years, or the fluctuation in temperatures be attributed to chance.

Conduct a hypothesis test at the 95% significance level, testing whether there has been an increase in temperatures over the years. Show all the steps of hypothesis testing explaining your choices in every step.

Explain your findings. Discuss what conclusions can be drawn from your findings. What, if any, variables may have affected your findings? What further tests could you carry out to support your findings?

**Section II**

This section is to be completed using MATLAB and original printouts have to be submitted with your report.

Euler’s Method

- In the Matlab command window, write a procedure using a
**while**loop OR a**for**loop that will solve the following problem:

Use Eulers method to find an approximate numerical solution to the initial value problem *y’ = 3x + y ^{2 }*where

Displaying your *x* and *y* values after each iteration.

- Create a script file using Euler’s Method that will prompt the user for the initial
*x*value, the initial*y*value, the*h*value and the final*x*value, that will solve the following DE:

(3+2 )+4 =6 +4

The script file should only print the final *x* and *y* values as well as the number of iterations used.

- Run the script file using the condition y(0)=1, a step size of 0.01 and a final x value of 2.

- Solve the following linear differential equation algebraically

(3+2 )+4 =6 +4 , y(0)=1,

using the Integrating Factor Method and find the exact solution to the DE when x=2.

- Comment on the accuracy of your Euler’s Method. Discuss what could be done to create a more accurate result using Euler’s Method.

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