Question

MyOriental is a new supermarket chain that specialises in imported Asian products. It has opened branches in several Australian cities over the past three years. The Chief Financial Officer (CFO) is keen to estimate and compare the daily revenue achieved in Perth, Darwin, Melbourne and Sydney where MyOriental has invested the most. Due to data availability, the CFO does not have the full record of daily revenues. A random sample of daily revenues for each location is all she has. Having understood that working with the population is not possible, the CFO asks you to apply statistical inference to conduct the analysis. (The dataset is given in the fourth sheet named “Daily revenue” in the provided Excel file Data.xlsx). Your answers should try to address the following:

1. Choose appropriate approaches to summarise the dataset and in non-technical terms, briefly discuss why you think the chosen approaches are appropriate.

Answer 1

Statistical inference

There are two type of statistical analysis

1) Descriptive statistics

2) Inferential statistics

Descriptive statistics

Descriptive statistics summarized data using graph and summary value such as means and quarter range. Descriptive statistics help us identifiy the relationship in patterns. Descriptive statistics do not draw the conclusion beyond the data we already have

Inferential statistics

Inferential statistics does allow us to draw the conclusion beyond the data we have to the population to which it was drawn

Defination of inference

The process of drawing conclusions about population parameters based on a sample taken from the population. Sample we collect from the population Here are the examples of population and samples. All the population voter of the new zealand samples is 1000 people we pick from the population and who are ask there opinion on the online survey. Thorugh the sample we can draw the conculsion.

There are three main idea under lying inference

1) A sample is likely to be a good representation of the population.

2) There is an element of uncertainty as to how well the sample represents the population  

3) The way the sample is taken matters

1) A sample is likely to be a good representation of the population.

Its reasonable to expect that a sample of a object from a population will represent the population. If 40% of Australia people believe that economy is getting worse then about 40% of the sample also believe it

2) There is an element of uncertainty as to how well the sample represents the population  

Sample will never be a perfect representation of a population from which its drawn. This is reason of sampling error. for example Let us assume 60% australia population and 40% australia population says economy is getting worse. If we took the sample of 1000 people how likely is it 50% or more of them says that they think economy is getting worse. We can work this out using probability theory or we can run simulation on a computer to see what would we expect from whole lot of samples and size 1000 taken from the population 40% thinking economy is getting worse from simulation theory its turn out to be correct that only 40% thinking to be correct & probabilty from simulation theory of 50% population saying economcy is getting worse is zero

3) The way the sample is taken matters

This principle relate to non sampling error. The sample must be representative of the population. This happen based when each person of think population as a equal chance of being selective in the sample. In natural  and manuacturing processes we may be able to take the random sample reasonable easily however, when a population consistent people this could be difficult and costly so we do the best we can

Graphic Methods

There are innumerable graphic methods to present data, from the basic techniques included with spreadsheet software such as Microsoft Excel to the extremely specific and complex methods available in computer languages such as R. Entire books have been written on the use and misuse of graphics in presenting data, and the leading (if also controversial) expert in this field is Edward Tufte, a Yale professor (with a Master’s degree in statistics and a PhD in political science). His most famous work is The Visual Display of Quantitative Information but all of Tufte’s books are worthwhile reading for anyone seriously interested in the graphic display of data. It would be impossible to cover even a fraction of the available methods to display data in this section, so instead, a few of the most common methods are presented, including a discussion of issues concerning each.

It’s easy to get carried away with fancy graphical presentations, particularly because spreadsheets and statistical programs have built-in routines to create many types of graphs and charts. Tufte’s term for graphic material that does not convey information is “chartjunk,” which concisely conveys his opinion of such presentations. The standards for what is considered junk vary from one field of endeavor to another, but as a general rule, it is wise to use the simplest type of chart that clearly presents your information while remaining aware of the expectations and standards within your chosen profession or field of study.