Estimation
Sample Proportions and Point Estimation
Sample Proportions
Let p be the proportion of successes of a sample from a population whose total proportion of successes is and let p be the mean of
Contingency analysis
! Test the independence of two or more categorical variables ! Well learn one kind: ! 2 contingency analysis
Music and wine buying
OBSERVED French music playing 40 German music pl
Discrete distribution Fitting discrete distributions
A probability distribution describing a discrete numerical random variable For example, ! Number of heads from 10 flips of a coin ! Number of flowe
Proportions
A proportion is the fraction of individuals having a particular attribute.
Example: 2092 adult passengers on the Titanic; 654 survived Proportion of survivors = 654/2092 ! 0.3
Probability
Hypothesis testing
Hypothesis testing asks how unusual it is to get data that differHypothesisthe nullnutshell from testing in a hypothesis.
about this population, say, are If the data would be quite
Probability
The probability of an event is its true relative frequency, the proportion of times the event would occur if we repeated the same process over and over again.!
A and B are mutually exclusi
Sample size 10 from Normal distribution with =13 and ! 2=16
2
Sample size 10 from Normal distribution with =13 and ! 2=16
Frequency!
1.5
Frequency!
5 10 15 20 25
2
1.5
1
1
0.5
0.5
X = 13.5 s 2 = 12.1
Two common descriptions of data
! Location (or central tendency)
Describing data
! Width (or spread)
Measures of location
Mean Median Mode
Mean
Y=
!
n
Yi n
i= 1
n is the size of the sample!
Mean
Y1=56
Sir Francis Galton The history of statistics has its roots in biology
Inventor of fingerprints, study of heredity of quantitative traits Regression & correlation
Karl Pearson
PolymathStudied genetics
BIOL 300: Biostatistics
Course web address: http:/www.zoology.ubc.ca/! ~whitlock/bio300/
Professor:! Dr. Michael Whitlock Professor Department of Zoology Office: 216 Biodiversity e-mail: whitlock@zool
The Poisson Probability Distribution
If In a binomial experiment you are interested in finding the probability of a specific number of occurrences takes place within a given specified interval (usuall
8-6: Testing a claim about a standard deviation or variance In section 7.5 we used the chi-square distribution to help us construct confidence intervals about the population variance and standard devi
7.5 Estimating a Population Variance
We have seen how confidence intervals can be used to estimate the unknown value of a population mean or a proportion. We used the normal and student t distribution
Lecture #7 Chapter 7: Estimates and sample sizes In this chapter, we will learn an important technique of statistical inference to use sample statistics to estimate the value of an unknown population
6-6 Normal as Approximation to Binomial
This section describes another interesting application of the normal distribution. In section 5-3, you learned how to find binomial probabilities. For instance,
Normal distribution
0.4
The normal distribution is very common in nature
f ( x) =
1 2!
2
e
#
( x # )
2
2
2
0.3 0.2 0.1 -2 -1 0 1 2 3
Human body temperature Human birth weight Number of bristles on a D
Inference about means
Because Y is normally distributed:
But. We dont know !
A good approximation to the standard normal is then:
Z=
Y ! Y ! = "Y "n
t=
Y! s/ n
t has a Students t distribution
Degrees
Comparing means
! Tests with one categorical and one numerical variable ! Goal: to compare the mean of a numerical variable for different groups.
Paired vs. 2 sample comparisons
Paired comparisons all
Probability Distributions Probability and Independence
Probability For an experiment we define an event to be any collection of possible outcomes. A simple event is an event that consists of exactly o
Practice Midterm II
Printable Key Problem 1 The South Lake Tahoe Police Department has charted the number of arrests over the past twelve months. The number of arrests per month that are made follows
M ath 201 P ractice M idterm I
Please work out each of the given problems. Credit will be based on the steps that you show towards the final answer. Show your work. Printable Key Problem 1 Categorize
Math 201 Practice Midterm 3
Please work out each of the given problems. Credit will be based on the steps that you show towards the final answer. Show your work. Printable Key Problem 1 A study was do
Math 201 Practice Final
Please work out each of the given problems. Credit will be based on the steps that you show towards the final answer. Show your work. Printable Key Problem 1 Match the followin
Lecture Notes For Most Math Classes Taught at Lake Tahoe Community College
http:/ltcconline.net/greenl/courses/LectureNotes.htm Example Course Syllabus (From Fall 2008) Index of Terms Videos on Projec
Hypothesis Testing
Hypothesis Testing
Whenever we have a decision to make about a population characteristic, we make a hypothesis. Some examples are:
>3
or
5.
5. Then we can think of our opponent sug
Descriptive Statistics
Sampling and Statistics
Statistics
We start the discussion in the natural way. We all have a general feeling about what statistics is. In the course of these lecture notes, we w
Researcher and statistician error
Publication bias
Papers are more likely to be published if P<0.05 This causes a bias in the science reported in the literature.
~8% of biomedical papers have substant
Regression
! Predicts Y from X ! Linear regression assumes that the relationship between X and Y can be described by a line
Correlation vs. regression
Regression assumes.
! Random sample ! Y is normal
Analysis of variance (ANOVA) ANOVA
Comparing the means of more than two groups ! Like a t-test, but can compare more than two groups ! Asks whether any of two or more means is different from any other