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Probability/Statistics Project

Probability/Statistics Project.

I’m trying to study for my Probability course and I need some help to understand this question.

In this project, you will conduct real-world data analysis.

Aim: The overall aim of this project is to analyze real-world data. The specific objectives are:

  • To sample one set of data from the real-world.
  • To summarize each set of data statistically.
  • To perform statistical chi-square test on data.
  • To describe the above steps, data, and results in a report.

Data Collection: Students will collect one set of data from the real world. Data will be collected from a large number of observations (at least 100) for a continuous random variable from a population that is suspected to be normally distributed. Examples of such data include the body weight of people, the circumferences of oranges, the extension length of rubber bands at the point at which they burst, etc.

Descriptive Statistics: Do the following:

  • Calculate the sample mean.
  • Calculate the sample standard deviation.
  • Calculate the quartiles Q1, Q2, and Q3.
  • Construct a histogram.

Chi-Square Goodness of Fit Test: Using a Chi-Square Goodness of Fit Test with a significance level of 0.05, test the hypothesis that data is sampled from a Normal Distribution with a population mean equal to the sample mean and a population standard deviation equal to the sample standard deviation. For the test, start with the data classes from your histogram and merge them to ensure each class has a sufficient number of observations. Then, calculate the following:

  • Numbers of observations in the data.
  • Class probability.
  • Class expected value.
  • Chi-square component values.

Finally, calculate the chi-square value, describe the degrees of freedom, and explain your conclusion. Note that since you are using the sample means and standard deviations, you will need to adjust your degrees of freedom accordingly.

Report: A written report is due and it must be submitted before the due date. The project report is to be written in clear English with complete sentences. Be sure to define all notations and include descriptions of all tables and figures in the text. Your report should include a cover page, three sections, and two appendices.

11-point font, single-spaced. In Section 1, describe the data collection process with enough detail that the reader could replicate the process. In Section 2, include the descriptive statistics in a table and the histogram in a figure. In Section 3, describe the chi-square tests with clearly stated conclusions and tables for the calculated values. Appendices I and II should include tables of you the raw data.

Probability/Statistics Project