Essay MATH1324: Introduction to Statistics – Mathematics Assignment Help

Assignment Task:

Assignment Instructions

1- You are required to select ONLY ONE MEASUREMENT from the dataset for this investigation. You must decide which measurement to deal with. You don’t need to include all variables.

2- Since males and females tend to have different body dimensions, you are required to investigate the normality assumption of the selected variable separately in men and women. Let’s say that you selected biacromial diameter measurement as a variable of interest. Then you should investigate if this measurement fits a normal distribution in men and in women separately. Keep in mind that there will be some cases in which men’s distribution may fit a normal distribution where else female’s distribution may not fit a normal distribution, or vice a versa.

3- You need to import this dataset into RStudio and tidy it up (e.g., you may need to define the variable sex as a factor and define labels for it) using R functions. 

4- You need to give summary statistics (i.e., mean, median, standard deviation, first and third quartile, interquartile range, minimum and maximum values) for your variable of interest separately in men and in women using R functions. 

5- Then you will use R to summarise the empirical distribution of body measurement separately in men and women and compare it to a normal distribution. You need to do this visually by plotting the histogram with normal distribution overlay.

6- You will end by discussing the extent to how your theoretical normal distribution fits the empirical data and make recommendations regarding the modeling of this body measurement.

Report Section Descriptions

The report will be in a reproducible R Notebook format with written sections, R code and output. The report will be composed of the following sections (see Template above). 

1. Problem Statement  [Plain text]: Write a clear and concise problem statement that guides your investigation. Explain which variable you choose and outline the approaches taken for normal distribution fitting.
2. Load Packages [R Chunk]: This section is not marked. 
3. Data [R Chunk]: Import the body measurements data and prepare it for analysis. Show your code.
4. Summary Statistics [R Chunk]: Calculate descriptive statistics (i.e., mean, median, standard deviation, first and third quartile, interquartile range, minimum and maximum values) of the selected measurement grouped by sex.
5. Distribution Fitting [Plain Text and R Chunk] : Compare the empirical distribution of selected body measurement to a normal distribution separately in men and in women. You need to do this visually by plotting the histogram with normal distribution overlay. Show your code.
6. Interpretation [Plain text]: Going back to your problem statement, what insight has been gained from the investigation? Discuss the extent to how your theoretical normal distribution fits the empirical data.