Task 1: Random data sample
Select a random sample of size 60 from the given 2338 lodgments in the Taxation lodgment data set for 2014. You will use this sample data to complete tasks 2 to 6.
Task 2: Descriptive statistics
Use data summary methods to describe the returns in your sample using seven variables. These seven variables are items 2 to 8 above. Do not use item 1, Id No.
Use an appropriate graphical and summary statistical technique, chosen according to the type of variable. Less appropriate/inappropriate techniques will receive fewer/no marks.
Choose your techniques from the following:
- Tabular techniques: frequency tables and grouped frequency tables.
- Summary statistics: mode, median, mean, standard deviation, range, coefficient of variation and interquartile range.
- Graphical techniques: pie chart, bar graph, histogram, frequency polygon.
Do not draw an ogive curve, stem plot or a box plot in this assignment, and do not draw 3D graphs.
Use the following guidelines to assist you:
- For a nominal or an ordinal variable, draw a graph and present a frequency table in percentages.
- For a ratio or an interval variable, draw a graph and a summary statistics table, including summary statistics appropriate to the type of distribution only.
- Try to use variation in drawing graphs e.g. pie chart/bar chart or histogram/polygon.
- Do not draw two different graphs for the same variable. You can draw the same type of graph for two variables.
- Do not include any information that you will not include in your discussion such as kurtosis.
- Display and describe one variable at a time.
Task 3: Confidence intervals
Estimate the following quantities, using 95% confidence intervals and explain the meaning of your confidence intervals.
- The average salary/wages amount for agent lodged returns only
- The average work-related deductions for all sample lodgments.
Compare both intervals with their respective true means by calculating the actual population mean for the full 2338 lodgments. Then comparing the true population mean to the sample mean and confidence interval. It is not usual to do this, however you are required to do this for the purpose of this assignment.