Statistics Engineering Probability Project Report

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ENGINEERING PROBABILITY PROJECT 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. 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 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 Class Probability Calculate using Expected Frequency (ei) For each class, observations based on your collected data. n the assumed probability distribution. 1.0 take its probability and multiply by n. n 2 Class Component (o − e )2 i i ei 2 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 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.
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Engineering Probability Project
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ENGINEERING PROBABILITY PROJECT: OUTLINE

Project Part 1: Normal Distribution









Definition of Variable
Data Collection
Data Set
Descriptive Statistics
Box and Whiskers Plot
Frequency Distribution Table
Histogram
Chi-square Goodness-of-Fit Test

Project Part 2: Exponential Distribution









Definition of Variable
Data Collection
Data Set
Descriptive Statistics
Box and Whiskers Plot
Frequency Distribution Table
Histogram
Chi-square Goodness-of-Fit Test

Appendix



Project Part 1: Normal Distribution
Project Part 2: Exponential Distribution

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ENGINEERING PROBABILITY PROJECT
PROJECT PART 1: NORMAL DISTRIBUTION
Definition of Variable: The data below are the synthetic records of height of 18 years old
children.
Data Collection: The data were gathered on 1993 by a Growth Survey of 25,000 children 18
years of age recruited from Maternal and Child Healthcare Centers (MCHC) and schools. Only a
random sample of 200 individuals were included in this list. The researchers did a simple random
sampling to gather the 25,000 data, but since the number of participants is too large to replicate,
other researchers who want to replicate the experiment should do a simple random sampling of a
smaller number of participants and measure the height of the participants, in this case, 18-yearold children.
Data Set:
Height(Inches)
65.78
71.52
69.4
68.22
67.79
68.7
69.8
70.01
67.9
66.78
66.49
67.62
68.3
67.12
68.28
71.09
66.46
68.65
71.23
67.13
67.83
68.88

63.48

66.88

65.27

68.42

67.7

70.84

67.63

69.82

69.92

67.21

69.09

64.29

70.84

69.91

68.25

67.49

67.33

66.36

66.53

70.27

68.36

65.44

69.1

65.48

69.52

65.38

69.72

65.81

70.18

67.73

67.82

70.41

68.64

70.6

66.54

66.78

71.8

66.36

70.05

69.21

67.54

66.28

66.8

66.5

69.2

67.66

69

69.13

67.81

68.3

67.36

64.05

67.01

70.09

68.57

70.81

70.18

65.18

68.22

68.23

69.66

69.06

68.13

67.97

67.73

70.24

65.98

67.22

71.49

68.67

67.37

69.2

70.06

67.21

68.71

66.81

70.56

69.42

68.89

66.89

66.29

68.94

69.54

65.74

63.43

67.94

67.4

65.98

66.77

65.63

66.48

66.58

68.89

66.5

66.01

67.11

64.87

67.93

72.44

65.87

67.09

68.89

64.13

66.78

68.35

70.24

70.98

68.74

65.61

68.27

67.5

66.23

67.76

71.23

7...


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