Lecture 5. Binomial Distribution
Bernoulli trials experiments satisfying 3 conditions:
1. Experiment has only 2 possible outcomes: Success (S) and Failure (F).
2. The probability of S is fixed (does not change) from trial to trial.
P(S)=p, 0<p<1, P(F)= 1-
Lecture 11: BIVARIATE DATA: CORRELATION AND REGRESSION
Two variables of interest: X, Y.
GOAL: Quantify association between X and Y: correlation.
Predict value of Y from the value of X: regression.
EXAMPLES: (height, weight), (yrs. of education, salary), (
Lecture 4. CONDITIONAL PROBABILITY and INDEPENDENCE
In many experiments we have partial information about the outcome,
when we use this info the sample space becomes smaller.
EXAMPLE. Roll a die. Events: A: score is odd=cfw_1, 3, 5. B: score is 2.
Lecture 7: ESTIMATION AND CONFIDENCE INTERVALS
Up to now we assumed that we knew the parameters of the
Example. Binomial experiment
Sampling from a normal population
knew probability of success p.
knew mean and st. dev.
In practice paramete
LECTURE 6. SAMPLING DISTRIBUTIONS. SAMPLING VARIABILITY
COMMON NEED: estimate population parameters: mean or proportion or
E.g. Producers of clothing need to know average dimensions of human
body and their variability. Food industry needs to know a
Lecture 2. Descriptive Statistics: Measures of
summarize or describe the important characteristics of a
known set of data
use sample data to make inferences (or generalizations)
about a population
Lecture 9: LARGE SAMPLE TESTS ON PROPORTIONS
Binomial experiment with n trials and unknown proportion of
Ho: p=p0, where p0 is a specified, known value.
DATA: Observe x successes, get sample proportion of successes
Lecture 8: CONFIDENCE INTERVAL FOR MEAN WITH UNKNOWN
If the population variance is unknown, estimate it using the
sample variance S:
( xi x ) .
n 1 i =1
Then, replace with S in the Z-statistic used for the confidence
METHODS FOR: COLLECTING, SUMMARIZING,
ANALYZING, INTERPRETING DATA
WHY STUDY STATISTICS?
To understand info involving chance polls,
advertising, sports, science, etc.;
To read/do research results: tables, graphs, reports;
To develop analytic, critical t
Lecture 10: Comparing two populations: proportions
Problem: Compare two sets of sample data: e.g. is the proportion of As in
this semester 152 the same as last Fall?
Methods: Extend the methods introduced for situations involving one
sample to the new sit
Lecture 3. Measures of Relative Standing and
Exploratory Data Analysis (EDA)
Problem: The average weekly sales of a small company are
$10,000 with a standard deviation of $450. This week their
sales were $9050. Is this week unusually low?
Measures of rela