Continuous Distributions- Statistics

Mathematics

Statistics

Western Governors University

Question Description

Instructions

Continuous random variables are interesting to study and appear in all kinds of applications. The height of basketball players on a professional team, ACT scores, bone density test scores, baseball averages, IQ scores, and the length of time you wait for a bus are just a few examples of continuous random variables. This assessment allows you to collect data on any continuous random variable that is interesting to you! You will conduct a survey to collect your data, fit the data you collect to various distribution models, and validate the central limit theorem.

Survey Procedures

  • Decide what continuous, quantitative data you are going to study.
  • Describe your sampling method in detail and why you chose that method. You may use cluster, stratified, systematic, or simple random sample using a random number generator, but do not use convenience sampling. If you have another method you would like considered, please contact your instructor for approval.
  • Create your survey.
  • Conduct a mock survey. Your data size must be at least 150.
  • Summarize your data in a meaningful way. Include the following information:
    • Define your random variable (X) in words
    • Create two lists of your data: unordered data (how it was collected) and in order from smallest to largest

Data Analysis
  • Find the sample mean and standard deviation (round to 2 decimal places)
  • Construct a histogram of your data containing six to ten intervals of equal width. Include labels and scales. Describe the shape of your data.
  • Look at three possible distributions of continuous data: Uniform, Exponential and Normal. Which does your data most closely resemble based on the theoretical graphs for these distributions? Discuss and explain your decision. Include a graph of the theoretical distribution you choose.
  • Calculate the value K (an X value) that is 1.85 standard deviations above the sample mean.
  • Using your ordered data set, determine the relative frequencies (round to 4 decimal places) for the following:
    • X < K
    • X > K
    • X = K
  • Based on the distribution you chose that best fits your data, find the following theoretical probabilities (round to 4 decimal places)
    • P(X < K)
    • P(X > K)
    • P(X = K)
  • Compare your relative frequencies to the corresponding theoretical probabilities. Use this in your discussion of how your data fits the distribution you chose.

Assignment Checklist
  • Title Page
  • Written report on procedures and findings. This includes the explanation of the continuous, quantitative random variable you are studying, a description of the population under study, the sample, and your survey procedures. Include all your answers to the above questions. Be sure to include the information listed under Data Analysis.
  • Data Collected and Reported. Two lists of your data: unordered data and in order from smallest to largest. On this page include the sample mean and standard deviation.
  • Graphs to include a histogram of your data along with the graph of the theoretical distribution that is the best fit for your data.

Format
  • doc, docx, xls, xlss
  • Style: APA
  • Length: 4-6 pages

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