engineering probability data report

IE 3301-004 Spring 2018 PROJECT Part I: Due Friday, May 10 by 11:59pm via Blackboard SafeAssignment

Students will complete 2 parts to a project for the semester. Each submission is individual and should not be shared with other classmates. Aim: The overall aim of these projects is to analyze real-world data. The specific objectives are:

1. To sample one set of data from the real-world. 2. To summarize each set of data statistically. 3. To perform statistical chi-square tests on the collected data set. 4. To describe the above steps, data, and results in a report.

On the cover of each Project Part report, please transcribe the following statement:

“I _________________ did not give or receive any assistance on this project, and the report submitted is wholly my own.”

Write your name in the blank and sign below it. You may use an electronic signature, such as Adobe Sign. Tasks for Part I Data Collection: Students can select to collect one real world data set. You can focus on one of the two data collection options. Option 1: data set can be collected from a large number of observations (at least 60) 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. Option 2: data set can be the inter-arrival time of a sequence of 60 or more events. First, record the actual clock time (to the nearest second) of each of at least 60 consecutive events, such as the actual time that a customer enters the post office. Then, determine the interval between occurrences by taking the difference between successive event times. Consequently, the data set will comprise of at least 59 inter-arrival times. You may use 'second' as a unit of time. You can ask instructor for data collection comments and suggestions to ensure the relevance, quality and accuracy of your data. Descriptive Statistics: For the collected data sets, use software to do the following:

• Calculate the sample mean and sample standard deviation. • Calculate the quartiles Q1, Q2, and Q3. • Construct a box-and-whisker plot. • Construct a frequency table. • Construct a frequency histogram.

Report: 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. To improve your writing, you should consider taking your report to the UTA Writing Center. Your report should include a cover page, the following sections, and two appendices:

I. Data. Describe the data collection process with enough detail that the reader could replicate the process. You should include tables of your raw data values.

II. Descriptive Statistics: Include and explain your descriptive statistics analysis. Interpret the results of the analysis using your data application topic, and test the data distribution. For example, if the data set appear to follow a Normal Distribution? If the data set appear to follow an Exponential Distribution?

Tasks for Part II 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 Set in Option 1 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. Similarly, if select the Option 2, you can test the hypothesis with a significance level of 0.05 that the data is sampled from an Exponential Distribution with a population mean equal to the sample mean. For the hypothesis test, start with the data classes from your histogram and merge them to ensure each class has a sufficient number of observations. Then, for each data class, calculate the following:

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

Finally, for each test, calculate the chi-square value, describe the degrees of freedom, and explain your conclusion. EXAMPLE SETUP

Class Observed Frequency (oi)

Class Probability Expected Frequency (ei)

χ2 Class Component

X ≤ 2 Count observations based on your collected data.

Calculate using the assumed probability distribution.

For each class, take its probability and multiply by n.

2 < X ≤ 7 7 < X ≤ 12 X > 12 Total n 1.0 n χ2 statistic

Report: 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. To improve your writing, you should consider taking your report to the UTA Writing Center. Your report should include a cover page and the following additional section:

2( )i i i

o e e −