Engineering Statistics Assignment

Data Collecting Project -

Introduction

Overview:

It is essential for a course about applied statistic, like the course of IE332, to have assessment tools which examine the ability of the students to apply the statistical techniques and methods in different manufacturing and industrial situations.

This 4-students group project will be submitted to the students in the beginning of the semester to motivate them to know how they can collect data correctly in real situations and what conclusions they can draw from their calculations and graphs.

This project will be graded by 5% of the total marks of the course and will be submitted with the Mid-term Practical Exam Report by email. For any group fail to submit their report by the due date, there will be 2% deducted from the deserved marks for every day of lateness. Any late report will NOT be accepted after 1 week of the due date.

Objectives of this project:

1. Encourage the students to work as team.

2. Encourage the students to share their knowledge about the course.

3. Motivate the students and examine their ability to apply the statistical methods correctly.

4. Motivate the students to ask themselves what conclusions we can draw from these results.

5. Examine the ability of the students to display their works in a form of a technical report, to organize meetings and distribute the tasks among the team members, to write the meeting minutes and to show evidences about their work.

6. Encourage the students to collect their own data based on experiment from their own mind (consistency with logic and engineering sense is essential).

7. Motivate the students to move from memorize the topics to the world of thinking as professional engineers.

Data:

Usually, in the engineering environment, the data are almost always samples, that have been selected from real populations by one of three ways: retrospective studies based on historical data, observational studies or designed experiments.

In this project, each group will collect their own data for one question, to be familiar with the method of collecting data.

Notes:

1. Write the solution of this project in a form of ONE report and type it by using Microsoft Word.

2. Submit the report and the Minitab file to the instructor by email before the due date. There is 2% deduction for every day of lateness.

3. Write the solutions of the questions as decimal numbers (4 digits after the decimal point for probability {e.g. 0.0000} and 2 digits after the decimal point for other numbers {e.g. 0.00} and use comma for every 3 numbers before the decimal point, i.e. period {e.g. 0,000.00}).

4. Write your comment and interpretation at the end of each question.

5. Print, scan and attach any set of data, calculation, graph, solution or output by Minitab or Excel.

6. To attach any table, figure or chart, scan, copy and paste it in the file.

7. Display evidences about conducting the experiment and attending the meetings by all the members by attach photos and meetings minutes.

Q1. Decide to conduct a real data collection relating to any case you have learned from chapter 9 or 10 for one population or two different populations.

1. Which experiment you have chosen and what is/are the population(s).

2. Explain which data you have collected. [Note: You have to collect the data by yourselves].

3. Which conditions and assumptions you have used for collecting the data to increase the precise of the data and keep its randomness [Methodology].

4. Which tools or devices you used for collecting the data.

5. What is the sample size? Why?

6. Collect the observations. List your data in a table.

7. Display the data in an empirical distribution form and charts. Laterin the Mid-Term Project, determine the estimation or do the test that you have conducted this experiment for it.

Mid-Term Practical Exam -

Introduction

Overview:

It is essential for a course about applied statistic, like the course of IE332, to have assessment tools which examine the ability of the students to apply the statistical techniques and methods in different manufacturing and industrial situations.

This 4-students group project will be submitted to the students in the middle of the semester to motivate them to display how they can apply what they have learned in this course correctly in real situations and what conclusions they can draw from their calculations and graphs.

This project will be graded by 15% of the total marks of the course and the due date to submit the solution report of this project by email will be after 2weeks from the assigned date. For any group fail to submit their report by the due date, there will be 2% deducted from the deserved marks for every day of lateness. Any late report will NOT be accepted after 1 week of the due date.

Objectives of this project:

1. Encourage the students to work as team.

2. Encourage the students to share their knowledge about the course.

3. Motivate the students and examine their ability to apply the statistical methods correctly.

4. Examine the students about the whole concepts and curriculum of the statistics courses in one project which integrate all the topics in one practical exam.

5. Teach the students by practice to use statistical software, such as Minitab and Excel, to analyze the data.

6. Motivate the students to ask themselves what conclusions we can draw from these results.

7. Examine the ability of the students to display their works in a form of a technical report, to organize meetings and distribute the tasks among the team members, to write the meeting minutes and to show evidences about their work.

8. Motivate the students to move from memorize the topics to the world of thinking as professional engineers.

Data:

Usually, in the engineering environment, the data are almost always samples, that have been selected from real populations by one of three ways: retrospective studies based on historical data, observational studies or designed experiments.

In this project, however, the instructor will use the Minitab software programto generate different sets of random data, follow predetermined probability distributions, to examine how each group can deal with engineering-based problems and how can they apply the statistical methods correctly and which conclusion can they draw from them. In addition, each group will use their own collected data for one question, to be familiar with the method of collecting data.

Notes:

1. Write the solution of this project in a form of ONE report and type it by using Microsoft Word.

2. Submit the report and the Minitab file to the instructor by email before the due date. There is 2% deduction for every day of lateness.

3. Write the solutions of the questions as decimal numbers (4 digits after the decimal point for probability {e.g. 0.0000} and 2 digits after the decimal point for other numbers {e.g. 0.00} and use comma for every 3 numbers before the decimal point, i.e. period {e.g. 0,000.00}).

4. Write your comment and interpretation at the end of each question.

5. Print, scan and attach any set of data, calculation, graph, solution or output by Minitab or Excel.

6. To attach any table, figure or chart, scan, copy and paste it in the file.

7. Display evidences about conducting the experiment and attending the meetings by all the members by attach photos and meetings minutes.

Mid-Term Project

Q1. a. Based on the data you have collected in the previous project, determine the estimation or do the test that you have collect that data for it.

b. Assume that the data stored in column A represent the strength, in gigapascals (GPa), of 60 specimens of aluminum alloy.

i. Complete the following frequency distribution for this data.   

[Note: Use suitable number of classes and class width. Number of classes or rows should be between 5 and 15 inclusive].

ii. Construct a frequency histogram of the data.

iii. Test the goodness of fit between the observed frequencies and the corresponding expected frequencies of a normal distribution with suitable µ and σ, using a 0.045 level of significance. Use the following table:

iv. Construct a normal probability plot for the data as follow:

1. Manually on a copy from page 3 of Table 18. Use the table in page 1 of Table 18.[Note: Scan and attach the table and the chart on your report].

2. By using Excel on a chart like that in page 2 of Table 18.

3. By using Minitab.

Then, compare between plots. And Comment on the normality of your data.

v. By using the figure in Table 17, make the calculations to decide the most suitable form of the distribution of the data. And Comment. Attach the figure and position your point on it.

c. Assume that the data stored in column B represent the lifetime, in years, of 50fuses in a certain application.

i. Construct a normal probability plot for the data by using Minitab.

ii. By using the figure in Table 17, make the calculations to decide the most suitable form of the distribution of the data. And Comment. Attach the figure and position your point on it.

Q2. Assume that the data stored in column C represent the diameters, in mm, of 40 ball bearings manufactured by a certain process. Assume that process manufactures ball bearings whose diameters are normally distributed. Assume the population standard deviation is 0.03mm.

a. Compute a 96%confidence interval on the mean of the diameters of the ball bearings. And Comment.

b. How large a sample is needed if we wish to be 96% confident that our sample mean will be within 0.01 mm. of the true mean? And Comment.

c. Generate the additional number of data necessary, based on part (b), by using Random Data function in Minitab 17. [Hint: Distribution: Normal, Parameters: µ = 30 mm., σ = 0.03 mm.]

Then, combine the generated data with the data in column C in column D.

d. Based on the data in column D, compute a 96%confidence interval on the mean of the diameters of the ball bearings.

Is the maximum error of the mean of the ball bearing's diameters, when the confidence level is 96%, is less than 0.01 mm. as required. And Comment on the maximum error and the new value of x ¯.

From here, continue based on the data on column C.

e. Compute a 94% lower confidence bound for the mean of the diameters of the ball bearings. And Comment.

f. Test the hypothesis that μ=30.05 mm. against the alternative hypothesis μ≠30.05 mm., at the size of the test = 0.05. And Comment.

g. How large a sample is needed if we wish the power of the test that μ=30.05 mm.against the alternative hypothesis μ≠30.05 mm., at α = 0.05, is 0.9 to detect a difference of 0.01 mm. between the true mean and the hypothesized mean. And Comment.

h. Suppose the 40 observations in the data set are supplemented by a 41th value of 31 mm. In the context of the original 40 observations, is the new value an outlier? Justify your answer. Use a 0.06 level of significance.

i. Compute a 95% tolerance limit of the diameters that is exceeded by 90% of the ball bearings. And Comment.

j. Test the hypothesis that σ=0.04mm. against the alternative that σ<0.04 mm. by using a P-value approach. And Comment.

Q3. a. A study was made to compare the strength of two kinds of thread under similar conditions. 20 pieces from type A and 18 pieces from type B are tested.

Assume that the data stored in columns E &F represent tensile strength, in kilograms, of the pieces of thread from type A and type B, respectively.

i. Test the equality of the variances. Use a 0.065 level of significance. And comment.

ii. Based on the data and part (i), are type B has tensile strength, on average, higher than that of type A. Use a 0.04 level of significance. Comment, and then compare the results with Minitab results.

iii. How large both samples are required if the examiner wants the power of the test to be 0.90 when the difference between the true difference between means and hypothesized difference between means is 1.4σ. Assume σ₁&σ₂ are unknown but they are equal. Use α = 0.05. Determine:

1. By using the Table 10.

2. By using OC curves Table 16 (f). Attach the OC Curve Fig. [Note: the y axis in the OC curve is β).

3. By using Minitab. [Note: Use σ ≈ Sp and difference = 1.4*Sp].

And then compare between the results of the three methods. Justify the difference if there is a difference.

b. An experiment was conducted in a windy day, where the wind speed was 70 km/hr., on an airport runway to study the effect of the wind on the acceleration of the motorcycles under similar conditions. 16 motorcyclists are asked to drive their motorcycles to the highest speed twice, one with the wind direction and the other against it and record the highest speed after 10 sections from the departure time in each case. Assume that the data stored in columns G &H represent the motorcycles' highest speed, in km/hr., in the two cases, respectively.

i. Use the data stored in columns G &H in the following table:

ii. Find a 91% confidence interval for the difference between means for paired observations. Assume the distribution of the differences to be approximately normal. What conclusion can you draw from the results? Is there a significance difference?

Assume that the data stored in columns I&J represent the numbers of days that male and female employees in a certain company, selected randomly, were absent during last year, respectively.

i. Find a 92% confidence interval for the true proportion of male employees who does not be absent for more than 5 days.[Note: Use method 1]. And comment.

ii. Test the hypothesis that the proportion of male employees who does not be absent for more than 5 days, p1, is higher than the proportion of the same group in female employees, p2. Use a 0.06 level of significance. And comment.

Q4. a. Assume that a survey is conducted on Saudi International airports where 500 passengers are asked about his original city. The data in columns K &L represent the international airport the passenger used and his original city, respectively.

i. Use the data stored in columns K &L in the following table:

ii. Test the hypothesis, at a 0.04 level of significance, that the passenger's city and the international airport that he used is independent. And comment.

b. Assume that a study about improving the education in Saudi Arabia is carried out, the researcher has decided, in advance, to select certain numbers of students from each of the schools (public, privates and international) and ask each student about his opinion about the new suggestion of requiring a TOEFL certificate to be admitted into the universities.

The data in columns M &N represent the type of the student's school and his opinion, respectively.

i. Use the data stored in columns M &N in the following table:

ii. Test the hypothesis, at a 0.07 level of significance, that opinions concerning TOEFL certificate are the same within each group of schools' students (Test of homogeneity). And comment.

c. A company has three sales offices in Riyadh, Jeddah and Al-Dammam. The sales manager wants to compare the performance of the offices.

The data in columns O, P&Q represent the results of the call or the meeting with the clients for Riyadh, Jeddah and Al-Dammam offices, respectively.

i. Use the data stored in columns O, P&Qin the following table:

ii. Test the hypothesis, at a 0.03 level of significance, that the three offices having the same percentage of deals. And comment.

Attachment:- Assignment.rar