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 is
1) identify an interval of values likely to contain

Data: Displays and Summary
Statistics
ST 515
January 11, 2015
Displays for Continuous Data
Stem-and-leaf plot
Dot plot
Scatterplot
Time-sequence plot
Histogram
Boxplot
preserve data
emphasize shape
Stem-and-Leaf Plot
Suppose that we have data that cons

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 population
mean
Confidence intervals for proportions

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
Clinical trial-placebo vs. drug
Each outcome of experiment i

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 Airplane Reverse Thruster was fine. A new thruster is
ins

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 characterized by a X and
its dist (can be discrete or continuous)

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 Region
Significance Level
Critical value
P-value
Typ

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 data to calculate an
estimate of the value(s) of the p

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 value) of the
population model is +1
.
+1
= m1 ( + 1)

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(A or B) = P(A) + P(B) P(A and B)
P(A and B) denotes th

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 of 100, the complication rate
would fall between 2.5% an

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
Hypothesis test for mean when is known (H0: = 0)
'(
wi

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 just a collection
of numbers.
The Ws
A context is defined

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-axis).
The response variable goes on the vertical axis
(

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 Region
Significance Level
Critical value
P-value
Typ

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
2 Means
2 Proportions
Examples:
Test the claim that

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 population
mean
Confidence intervals for proportions
Boo

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,b)
1
= (
2
2
ution.
0
1
3
x
3
Uniform Distribution
d

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: Minimum, Q1, Median, Q3, Maximum
standard deviati

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 card from a deck
Ex: Test the breaking strength of fishi

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 prohibitively expensive to talk
to/measure every unit
Sample

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
4
5
6
7
P(x) 0.01
0.03
0.13
0.25
0.39
0.17
0.02
#Reg 15

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: Minimum, Q1, Median, Q3, Maximum
standard deviation:
va