Description

Project 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:

To sample two sets of data from the real-world.

To summarize each set of data statistically.

To perform statistical chi-square tests on each set of data.

To describe the above steps, data, and results in a report.check the attached files to see detail.You need to use data from https://www.kaggle.com/.IE 3301 PROJECT

Fall 2022

Due: Friday, Nov 25th by 11:59pm via Canvas

Project 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.

2.

3.

4.

To sample two sets of data from the real-world.

To summarize each set of data statistically.

To perform statistical chi-square tests on each set of data.

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 1

Data Collection: Students will collect two sets of data from the real world. Set 1 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 adult males, the circumferences of oranges, the extension length of rubber bands

at the point at which they burst, etc. Set 2 will be the inter-arrival time of a sequence of 100 or

more events. First, record the actual clock time (to the nearest second, e.g. 2:43:18pm) of each

of at least 100 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, Set 2 will comprise of at least 99 inter-arrival times. You may use

‘second’ as a unit of time.

Descriptive Statistics: For both Sets 1 and 2, 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 typewritten 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 for Sets 1 and 2 with enough detail that the reader

could replicate the process. Appendices I and II should include tables of your raw data for

Sets 1 and 2, respectively. The raw data for Set 2 should consist of the recorded actual clock

times.

II. Descriptive Statistics: Include and explain your descriptive statistics analysis. Interpret the

results of the analysis using your data application topic. Does Set 1 appear to follow a

Normal Distribution? Does Set 2 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 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

X≤2

2 12

Total

Observed

Frequency (oi)

Count

observations

based on your

collected data.

n

Class Probability

Calculate using

the assumed

probability

distribution.

1.0

Expected

Frequency (ei)

For each class,

take its

probability and

multiply by n.

n

χ2 Class

Component

(oi − ei ) 2

ei

χ2 statistic

Report: The project report is to be typewritten 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:

Goodness-of-Fit Tests: Describe the chi-square tests with tables for the calculated values and

clearly stated conclusions. Show the Excel formulas for your table calculations in an Appendix.

Sample Format

PROJECT PART I (INTER-ARRIVAL TIMES)

RAW DATA

Data Values: Arrival time of customers at a Bank

Interval (Inter-arrival time): Time difference between

arrival times oftwo Successive Customers (in Minutes or

Seconds)

Data Set:

Time

Interval

.

.

.

.

Mean:

Standard Deviation:

Time

Interval

Time

Interval

Frequency Table

Histogram

BOX PLOT Chart

Quartile Values of X :

Q1:

Q2:

Q3:

(SAMPLE FORMAT)

PROJECT PART II

Expended Frequency Table:

INTERVAL

OBSERVED

FREQUENCY

CLASS

PROBABILITY

The class probabilities are:

Sample Mean: and Sample Standard Deviation:

FORMULAS TO CALCULATE P(X

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