Inference: One Sample
Confidence Intervals
ST 515
February 24, 2016
Goal
In general, the values for parameters in a population model
(data-generating process) are unknown. Based on data, the
object
Sampling Distributions
ST 515
February 17, 2016
Population & Random Samples
Population = cfw_all (potential) obs we are
interested
Population can be finite or infinite
Population can be characteriz
Inference: One-Sample
Hypothesis Testing
ST 515
March 2, 2016
1
Goals and Objectives:
Goals:
To understand and find the following:
Null Hypothesis
Alternative Hypothesis
Test statistic
Critical
Inference: Point Estimation
Chapter 6
ST 515
February 17, 2016
Point Estimation
Suppose we have a model for a population
and a random sample of data from the
population.
We would like to use the
Midterm Exam 2
March 16, 2016
1. Suppose that we have a probability density function
(
x1 if 0 < x < 1
f (x) =
0
otherwise
(a) (5 points) Find the method of moments estimator for . The mean (expected
Probability
ST 515
January 23, 2016
General Rule (Intuitive)
Finding P(A or B)
Find total ways A can occur
Find total ways B can occur
Make sure not to count twice
Addition Rule:
2 cases:
1. P(
Stem-and-Leaf Plot Boxplot: 0-4, 5-9
Right skew: small value is more; left skew: big value is more.
IQR: Interquartile Range: Q3 + 1.5 IQR (upper fence); Q1 1.5 IQR (lower fence)
Five Number Summary:
Overview and Descriptive Statistics
Why would an engineer want to collect data?
You should know the meaning of the following terms:
Statistics (as a field of study) studies how to (a) collect data; (b
Probability
Sample spaces and events
Probability refers to the study of randomness and uncertainty. The discipline provides methods
for quantifying the chances associated with the various outcomes of
ST 515: Experimental Statistics for Engineers
Section 001, Fall 2017
451 Riddick Hall, Tu-Th 8:30-9:45 am
Instructor: Dr. Donald Martin ([email protected]), 4272 SAS Hall, (919)-515-1936
Office Hou
Continuous random variables and probability distributions
Random Variables
A random variable is continuous if it takes values in _.
Motivating example for probability density functions
In a study of t
Discrete random variables and probability distributions
Random Variables
A researcher may want to focus on a specific aspect of the experimental data. For example, they
may want to record only the num
Homework 1 Solution Key
Miao Yu
September 1, 2017
1.4 #58
The median is roughly same for these two machines. But the distributions differ markedly in other
respects. The plot of the first machine show
ST kl: Hamamh L solution
1% 1% 68 Let (<1. = rm/ct an aariane 4? I , A 2' tme (M airline #2
I3; 3 Crowd m afrm 5&3 . g. 1 Late, at LA , 32.: We at DC.
one; B: We at xatj one destinatn'an. 77m,
Milka-5
Ho:PlaneseemstomeetallstandardsofFAAand is ok-ed to fly.
Ha:PlaneseemstoNOTmeetallstandardsof FAA and is AOG (airplane on the ground).
Error Type 1 : (False- Positive) We reject Ho but in fact the Ai
Random variables and
probability distributions
ST 515
January 27, 2016
In an experiment there are several
characteristics that can be observed
Marijuana use over a year.
Satisfaction survey
Clinic
Inference: One Sample
Confidence Intervals
ST 515
February 29, 2016
Roadmap
Central limit theorem
Large sample confidence intervals for a population
mean
Small sample confidence intervals for a p
Data: Displays and Summary
Statistics
ST 515
January 6, 2016
What are data?
24, 30, 23, 40, 27, 25
Test scores?
Ages in a golf foursome?
Bib numbers for marathon runners?
Without context these are jus
Inference: Linear Regression and
Correlation
ST 515
April 4, 2016
Scatterplots
Which variable is associated with which axis?
The explanatory variable goes on the horizontal
axis (also called the x-ax
Inference: One-Sample
Hypothesis Testing
ST 515
March 2, 2016
1
Goals and Objectives:
Goals:
To understand and find the following:
Null Hypothesis
Alternative Hypothesis
Test statistic
Critical
Inference: Two-Sample Inference
ST 515
March 28, 2016
Preview:
Testing hypotheses and estimating values
for two sets of data
Confidence intervals 2 samples
Mean
Proportion
Testing a hypothesis
Inference: One Sample
Confidence Intervals
ST 515
March 2, 2016
Roadmap
Central limit theorem
Large sample confidence intervals for a population
mean
Small sample confidence intervals for a popul
Models: Continuous
Distributions
ST 515
February 10, 2016
1
Continuous Probability
Distributions
Cumulative distribution function
,
= = (
-.
Probability that X takes on a value in some
interval (a
Stem-and-Leaf Plot Boxplot: 0-4, 5-9
Right skew: small value is more; left skew: big value is more.
IQR: Interquartile Range: Q3 + 1.5 IQR (upper fence); Q1 1.5 IQR (lower fence)
Five Number Summar
Probability
ST 515
January 13, 2016
Probability
The study of randomness and uncertainty
Experiment: Any action or process whose
outcome is subject to uncertainty
Ex: Tossing a coin
Ex: Select a ca
Discrete Distributions
ST 515
February 3, 2016
1
2
Population and Sample
Population(Big Who)
Group of experimental units we want
information from.
Generally, very large.
Impractical or prohibit
Expectations and
Distributions
ST 515
February 1, 2016
Expectations
Consider a university with 15,000 students
and let X = number of courses which a r.s.
student is registered.
The pmf is:
x
1
2
3
Inference: Confidence Interval
and Hypothesis Testing Summary
ST 515
March 30, 2016
One-Sample, Mean and Proportion, Large Sample
Assumptions: n 25
Confidence interval for mean when is known
Hypo
CI: Based on our sample data, we are 95%
confident that the "true" complication rate at GHS
is between 2.5% and 17.5%. Another
interpretation: if we were to take 100 additional
samples, 95 times out o