Engineering Statistics notes

Data Analysis and Design of Experiments –
CHEE231 (3 credits)
Fall 2013
Department of Chemical Engineering
McGill University
Instructor : Prof. Pierre-Luc Girard-Lauriault
M.H. Wong Building, room 4150
Tel. [phone] email : [e-mail]
Co-Requisite: CHEE 291 - Instrumentation and Measurement 1
Teaching Assistants:
Simon Kwan ([e-mail]) - Assignments
Gregory Laskey ([e-mail]) - Assignments
Mahdi Roohnikan ([e-mail]) - Simulations
Website:
myCourses
Lecture 12 - CHEE 231 – Fall 2013 – Prof. Girard-Lauriault

1

16

Mid-Term 1

14

x = 57.3%

12

10

s = 18.1%

8

18.1 sx =
= 1.73%
108

6

4

2

0

Your z score:

M−x z= s

0

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Q1 : 44.5 %
Q2 : 58.0 %
Q3 : 69.0 %

Lecture 12 - CHEE 231 – Fall 2013 – Prof. Girard-Lauriault

2

Sampling Distribution, unknown Variance While we know that X is normally distributed (Central
Limit Theorem), it is important to have a good point estimate on σ to use the z distribution as a probability distribution function for X . Rule of thumb: If n≥30 the normal approximation will be satisfactory regardless of the shape of the population. (If n is evaluated from more than 30 values, we will consider that s is a good point estimate for σ.) Otherwise, we need to use a different shape of probability distribution function that will consider an error on σ.

Lecture 12 - CHEE 231 – Fall 2013 – Prof. Girard-Lauriault

3

Confidence Interval on the mean, small sample (n≤30) &
Variance unknown
Let X1, X2, … ,Xn be a random sample from a normal distribution with unknown mean and variance. The random variable: X −µ
T=
S