Probability Cheat Sheet (The Legal Version!) Basic Probability Formulas Word Or And Not Operati on Add Multiply Subtract General Rule PAB=P(A)+P(B)-P(AB) PAB=PABP(B) PA'=1-P(A) Special Case, Rule Mutually Exclusive, PAB=P(A)+P(B) Independent, PAB=P(A
Homework 3
due @9:05 April 10th, 2017
1. Use software to generate 200 normal random numbers with mean 5,
variance 2 (In R, you could use command: rnorm(200, mean = 5,
sd = sqrt(2). Then use software to plot QQ-plot (normal
probability plot) of these 200 n
Name Kg period12345678
AP Stats Ch 9 Testing a Claim. Practice Multiple Choice
1. ln formulating hypotheses for a statistical test of signicance, the null hypothesis is often
a statement 0 no effect or no difference.
B. the probability of observing the d
STAT 3704: Statistics for Engineering Applications, Fall
2016
Practice Exam 2
Use the following to answer Questions 1 2.
A national survey interviewed 3800 people ages 18 and older nationwide by
telephone. One question asked was the amount of gasoline the
Chapter 4
SECTION 4.2
Review: The process to get CI for a population mean ( known)
1. Check the simple conditions.
- The sample is simple random sample(SRS).
- Sample size is large enough to assume CLT.
- The mean is unknown but the standard deviation is
Chapter 4
SECTION 4.1
4.1 Introduction to Estimation
p
p
Population: the set of all
possible observations of
interest to the problem at
hand.
Sample: the part of the
A parameter is a numeric
quantity that describes an
important characteristic of a
popula
Using Your TI-83/84/89 Calculator for Hypothesis Testing:
The 1-Proportion z Test
Dr. Laura Schultz
Statistics I
The 1-proportion z test is used to test hypotheses regarding population proportions. This handout
will take you through one of the examples we
Stat 3704: Statistics for Engineering Applications
Midterm2 - Sample Test
Part I Multiple Choice & Short Answer
Please write down your answers in the Answer Table! Only answers in the Answer Table
will be accepted.
Answer Table
1.
2.
3.
4.
5.
6.
1. A clot
Chapter 4
SECTION 4.3
4.3 Hypothesis testing for a single mean with unknown variance
Recall: Variance known:
One-sided Z-tests
Two-sided Z-tests
Variance unknown:
One-sided t-tests
Two-sided t-tests
4.3.1 One sided t-tests
Consider the injection molding p
Chapter 4
SECTION 4.4
4.4 Tests for Proportions
When randomly sampling from a population with proportion p of
successes, the sampling distribution of the sample proportion p [p hat]
has mean and standard deviation:
p = p
p p
p =
p(1 p)
n
is an unbiased
Stat 3704: Stats for Engineering
Applications
Introduction/Chapter 1
1
Engineering Method
The heart of sound engineering practice is the engineering
method
2
Example: Strength of Filament
Consider a production process of a new kind
of filament. In the pro
Chapter 3
SECTION 3.2 3.3
3.2 Random Variables and Distributions
Random Variable: Y is a random variable if Y is a function that assigns a
real numbered value to every possible event in a sample space, S, of
interest
Use capital letters to denote random
Stat 3704: Stats for Engineering
Apps
1
CHAPTER 2: DATA DISPLAYS
Overview
2
Stemplot
Boxplot
Histogram
Time Plots
Introduction
3
What do we actually do with a data set when its
handed to us?
By observing visual summaries of the data, we can:
Determ
Stat 3704: Stats for Engineering
Apps
CHAPTER 3: MODELING RANDOM
BEHAVIOR
Overview: Probability
2
Statisticians use probability to model uncertainty.
Consider-these statements:
There is a 30% that our engineering design firm will get the Nissan
contract.
Box Plots
1
Purpose: To give a quick display of some important features
of the data.
Note: The box plot represents a distillation of the data.
The stem-and-leaf display only loses the time order of the
data.
The box plot loses some of the information
Al @Oneway Analysis of Data By group
74 I
T3
Data
'.-'2
TI
70 0
groun
JQuantiles
Level Minimum 10% 25% Median T555 90% Maximum
1 70 70 72 72.5 T3 74 74
2 TO 70 TI 72 72 74 T4
Inference for a Single Mean
STAT 3704
~4.3
Overview
Introduction
Hypothesis Test
Confidence Interval
Summary
2
Introduction
Consider a situation where we want to estimate the mean
value of a population.
For example, in our marble factory, the diamet
3.17 n = 8 batches dyed by the process
p = probability of a batch being rejected = .05
Y = number of batches being rejected out of 8.
Y is distributed as binomial (n = 8, p = .05)
a Pr(YSl) Pr(Y=O)+Pr(Y=])
(3 ) (-05)0 (-95)8 +( '1 ) (.05) (.95)7
.6634 + 2
4.44
a.
Oneway Analysis of Data By group
b. (1) H 0 : 1 = 2 H1 : 1 2
(2) t =
X1 X 2
S p n11 + n12
(3) = 0.1, df = 8+8-2=14, t14,0.05 = 1.761. Reject H 0 if | t |> 1.761
(4) X 1 = 72.375, X 2 = 71.75 , S p =
t=
72.375 71.75
= 1.06
1.1764 18 + 18
(8 1) 1.4
Homework 1
due @ 9:05am on February 13th, 2017
1
Exercise 1.12 Citrus Blight(Page 36)
2 Exercise 2.4(Page 48)
You can download this data set from Canvas VT (Data set is in hw1.2.jmp) OR import it by
yourself.
3
1) Give the Five-Number Summary, IQR, and th
Homework 2
due @ 9:05am on March 13th, 2017
In order to get full points for your homework, you need to show every step that you
get the result, in detail.
1. Exercise 3.17
2. Exercise 3.27 (Hint: Use Poisson distribution.)
1
3. Exercise 3.33
4. Exercis
1. QQ-plot shows a straight line.
2. QQ-plot does not show a straight line.
3. a) 5.81.960.7/ 3 = (5.008, 6.592)
b) n 1.960.7/0.2 ! = 47.06, so n = 48
4. Since we do not know the standard deviation, so we are going to use t-statistic.
!
mean = !
! = 2.328
3704 HW 1 SOLUTION
1. Exercise 1.12 Citrus Blight
a. Response: amount of blight
b. Factors:
i. Chemical spray categorical
ii. Amount categorical (no penalty if you write continuous)
c. Levels:
i. Chemical spray: A, B, C
ii. Amount: low, high
d. T
Kill/l Sea Yum HW l
1' that mg?rflim :tcuageop mpzfqloogx 313; at lm a) The response of interest would be the existence of citrus
chemical sprays (A, B, C) are being considered. Each chemical spray will be blight m the leaf samples
applied in two amounts
JMP Notes
(A Quick Reference Supplement to the JMP Users Guide)
These notes outline the JMP commands for various statistical methods we will discuss in class (and then some). Dont worry if
you dont understand technical terms like variance inflation factor
STAT 3704: STATS FOR
ENGINEERING APPS
Chapter 2: Data Displays
Introduction
What do we actually do with a data set when its handed
to us?
By observing visual summaries of the data, we can:
Determine the general pattern of data
Identify outliers
Check