Normal Distribution
 Graph must be symmetric, and bellshaped with mean in the center
 Uniform distribution
o Rectangular graph
o Each value has an equal probability
 Density curve
o Continuous distribution
o requirements
Area under curve = 1
All point
CONTINUOUS RV &
NORMAL DISTRIBUTIONS
density curves, N(,), QQ plots, z distribution
Density curves
graph of a continuous probability distribution, with
area of 1.0 and 0 f(x) 1.0
density
P(190)=?
P(>190)=?
The Normal Distribution, N(,)
P(X<x)
x
Assessing
SAMPLING DISTRIBUTIONS
centre, shape, and spread; CLT
The discipline of Statistics
conducting studies to collect, summarize,
analyze, and draw conclusions from data
Descriptive Statistics:
organization,
summarization, and
sample
presentation of data
Infer
RANDOM VARIABLES
Discrete RVs, Binomial distributions
Random variables (RV)
a variable which has a numerical outcome of a random
phenomenon (i.e. procedure)
Example: Let X be the RV equal to the number of students
who have a part time job, out of four. As
Characteristics of Data
 Center average
 Variation measure of how much data varies amongst itself
 Distribution shape of distribution of data
 Outliers sample values lie outside range of most of data
 Time
Frequency Distribution
 Has data values and
Inference about Two Proportions
 Requirements
o Both are SRS
o Independent samples from one population not related to samples from the other
In other words, samples dont have anything to do with each other
o For both sample, number of successes and numbe
Hypothesis
 Hypothesis statement about property of population
 Hypothesis test procedure to test that statement
 Use RARE EVENT RULE
o If PVALUE IS LESS THAN ALPHA, the assumption is not correct
o In other words, we reject the null hypothesis
Basics

Normal as Approximation to Binomial Distribution
PROBABLITIES
 Requirements
o SRS
o Conditions for binomial distribution satisfied
o Np>=5, nq>=5
 Notation for proportions
o P = probability in entire population
o Phat = sample proportion of x successe
Regression
o How to solve
+ episilon(i) REGRESSION EQUATION
Episilon is error term that shows how far each point is from the population regression line
Epsilon(i) ~ N(0, sigma(e)
Shows that
o Population regression points dont line up
o Concept of regres
Rare Event Rule
 Under assumption, probability of observed event (PVALUE) is small, conclude assumption is not correct
Fundamentals
 Event collection of results of procedure
 Simple event outcome that cannot be broken down
 Sample space all simple ev
Random Variables
 Random variable represented by X
o Single number value determined by chance
o Discrete RV finite/infinite COUNTABLE variables
o Continuous RV infinite values on a continuous scale
 Probability distribution graph/table/formula that give
Correlation
 Also called bivariate data
 Basic concepts
o Correlation relationship between 2 variables
o Use a scatter plot
X and Y represent a one of the two variables used and are plotted together
o Linear correlation coefficient (r) SAMPLE STATISTIC
Introduction
 Population
o the complete collection of all elements (or objects) to be studied
o A parameter
 Sample
o sub collection of members (data points, individuals etc) from a population
o A statistic
 Census collect data from everyone
 Data Obs
ANOVA
 What is it?
o Method for testing equality of three or more populations by studying sample variances
o Better than using two samples at a time because doing this multiple times will reduce the confidence
level (CL^trials)
Assumes independent tests
Biol/Stats 2244A Sample Test 2 Questions
1. Suppose that two meteorological experts, A and B, independently provide simple weather forecasts of
rain or no rain for the next day. They do this for 100 days, after which it is found that expert A predicted
co
Bio statistics 2244A
FINAL EXAM REVIEW
Christina Wang
December 28th, 2011
CHAPTER 1 NOTES
CHAPTER 1.1
Goal of survey is to collect data from a small part of a larger group so that we can learn
about the large group, i.e. take a sample to learn about the
Biol/Stats 2244A Sample Test 1 Questions
Question1.
A psychological survey asks subjects to rate their level of happiness on a scale from 1 (least happy) to
7 (most happy). Which term best describes the resulting data?
A.
census data
B.
nominal data
C.
ra