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.
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
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.
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.
doc, docx, xls, xlss
Length: 4-6 pages
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