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Project Part III 12/1/2024

45 Points Possible

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Details

Students will complete 3 parts to a project for the semester. Each submission is individual and should not be shared with other classmates. Any form of copying and pasting from other sources and projects will be reported to the UT Arlington Office of Student Conduct.

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

1. To sample two sets of data from the real-world. 2. To summarize each set of data statistically. 3. To perform statistical chi-square tests on each set of data. 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 (https://acrobat.adobe.com/us/en/sign.html) .

Tasks for Part III

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 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, test the hypothesis with a significance level of 0.05 that Set 2 is sampled from an Exponential Distribution with a population mean equal to the sample mean. For each 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 (o )

Class Probability Expected Frequency (e )

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 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 (http://www.uta.edu/owl/) . Your report should include a cover page and the following sections mentioned in rubric

i i

2

2

View Rubric

IE3301 Part III Rubric (1)

Criteria Ratings Pts

Report Organization

3 pts Full Marks Report is logically organized and reasoning is easy to follow. All elements are present. Document is neat and well laid out. Appearance aids understanding

0 pts No Marks

/ 3 pts

Chi-Square Goodness of Fit Test view longer description

19 pts Full Marks Explain in a sentence about your data, and in detail about Normal Distribution parameters, degrees of freedom, formulas, all the calculations for table and to do the Hypothesis testing, Clearly

0 pts No Marks

/ 19 pts

IE3301 Part III Rubric (1)

Criteria Ratings Pts

identify the number of classes, probabilities, expected frequencies, and any information as mentioned in class. Show specific examples of the calculations. Conclude based on Hypothesis testing and your conclusion based on the result from Part II.

Chi-Square Goodness of Fit Test view longer description

19 pts Full Marks Explain in a sentence about your data, and in detail about Exponential parameters, degrees of freedom, formulas, all the calculations for table and to do the Hypothesis testing, Clearly identify the number of classes, probabilities, expected frequencies, and any information as mentioned in class. Show specific examples of the calculations. Conclude based on Hypothesis testing and your conclusion based on the result from Part II.

0 pts No Marks

/ 19 pts

Appendix

4 pts Full Marks Excel formulas for your table calculations for Normal Distribution and Exponential Distribution.

0 pts No Marks

/ 4 pts

Late Penalty 0 pts Full Marks -5 for each day late

0 pts No Marks / 0 pts

Incorrect Format

0 pts Full Marks -1 Missing academic honesty statement -1 Missing/Incorrect Signature

0 pts No Marks

/ 0 pts

Total Points: 0

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