`
42
Confidence Intervals
Confidence Intervals are estimates of population parameters, a range (or interval) of values that
is likely to contain the true value with X% confidence. They are created to answer the question,
How good is our point estimate (me
`
42
Confidence Intervals
Confidence Intervals are estimates of population parameters, a range (or interval) of values that
is likely to contain the true value with X% confidence. They are created to answer the question,
How good is our point estimate (me
64
Chi Square Models
Assumptions for the Chi Square Models:
1. The data are obtained from a random sample.
2. The expected frequency for each category must be 5 or more; i.e., E 5 .
Multinomial
Characteristics:
1. The number of trials is fixed.
2. The tri
49
Hypothesis Testing
Means
I. Comparing a sample mean to a specific value, one sample:
1. Null Hypotheses:
1. Ho: a value The rejection region (all the alpha) is in the right tail.
2. Ho: a value The rejection region (all the alpha) is in the left tail.
Structure of Statistics
37
Random sample  inherent assumption for all statistical
models. A sample used in statistical analysis should be taken from a
welldefined population and in a manner to assure randomization; i.e.,
each member of the population is
22
Discrete Distribution
Expectation: the "settled down" version of the mean; idealized, generalized average
computed as follows:
k
k
i
1
i
1
E ( x) xi f ( xi ) where f ( xi ) Pcfw_ X xi OR E[ g ( xi )] g ( xi ) f ( xi )
If each point in the sample space
57
Linear Regression
(x ) 0 1 x1 2 x2 n x n
Model:
0 , 1, 2 , n are unknown parameters for the means of the
,
,
populations that correspond to given values for x1 , x2 , x n ;
is the value for random error.
where
Purposes: 1. relationships/association
For proportions:
Confidence Intervals
* Confidence intervals are used to answer with question,
How good is p at estimating p?
* Create a confidence interval, p E for proportions with level of confidence,
1 (in percentage) and interpretation, X% confident
Math 207 for the Class Project
1.
Class Project: Writing Center
Read over previous study posted on the class conference so that you know
what is expected.
This study will be of an interview form and/or a survey form, depending on
what we decide. We will o
28
Continuous Functions
Moments
1. The kth moment about the origin of the distribution of the continuous random variable
X whose pdf is f is given by:
b
'
k k f ( x)dx for domain, a x b
x
a
For k = 1, is the theoretical mean.
2. The kth moment about the
45
Testing Hypotheses
Introduction:
Terms . . .
hypothesis  a claim or statement that something is true (or believed to be true)
testing hypotheses  use of sample statistics to determine if the sample is significantly different
from the claim.
null hypo
61
ANOVA Analysis of Variance
Oneway ANOVA is used to compare three or more means; i.e.,
Ho : 1 2 k . If the null hypothesis is rejected, then there is a difference
somewhere; therefore, after rejecting the null hypothesis, follow the analysis with
eithe
61
ANOVA Analysis of Variance
Oneway ANOVA is used to compare three or more means; i.e.,
Ho : 1 = 2 = k . If the null hypothesis is rejected, then there is a difference
somewhere; therefore, after rejecting the null hypothesis, follow the analysis with
e
Math 207, Probability and Statistics
Spring Semester, 2010
Dr. Evelyn Bailey
Office hours: Posted weekly on the class conference
Reader: How to Lie With Statistics by Darrell Huff
Materials: Math 207 Notes (provided in a notebook for this class), a calcul
28
Continuous Functions
Moments
1. The kth moment about the origin of the distribution of the continuous random variable
X whose pdf is f is given by:
b
= x k f ( x)dx for domain, a x b
'
k
a
For k = 1, is the theoretical mean.
2. The kth moment about th
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Math 207, Probability and Statistics
Spring Semester, 2011
Dr. Evelyn Bailey
Office hours: Posted weekly on the class conference
Readers: How to Lie With Statistics by Darrell Huff
Super Crunchers by Ian Ayres
Materials: Typed formal notes with homework p