Ch 14 (Random Variable)
Recall:
1.
x+y x y
= +
a
a a
,
x+ y+z x y z
= + +
a
a a a
Definition 1 (Random variable):
A random variable X (capital X), is a variable whose values x (little x) are outcomes
Some Business Rules that need to be incorporated into the Data Dictionary
Make sure you read the comments listed on the next worksheet; these comments identify additional rules/guidelines.
Constraints
Ch. 3: Percentiles, Boxplots
& z-scores
Percentiles divide a data set into hundredths
or 100 equal parts
Data sets have 99 percentiles: P1, P2, P3, P99
Quartiles divide the data set into 4ths
Q1 = 2
Measures of Central Tendency
We describe a data set by examining its
shape, location and dispersion. Weve looked
at shape; now we look at location.
If we want to describe a set of data with one
number
Two Populations
We cannot pool the sample standard
deviations (s1 and s2) because we cannot
assume that they are two estimates from
the same population standard deviation ().
Thus, we use the non-pool
The Normal Distribution
The Coca Cola Company filling machines are
adjusted to pour 12 ounces of Coca Cola in each
12-ounce can. However, the actual amount of soda
poured into each can is not always 1
Sampling Distributions &
Estimation ( known)
We need the characteristics of the sampling
distribution for the sample means.
Then, we can find the probability of occurrence of
any particular event.
If
Proportions
What proportion of all registered voters believe
that Gov. Christie knew about BridgeGate?
What proportion of the population of
households has more than one wage earner?
(rho): proportion
Sampling Distributions
Mortality Tables permit Actuaries to
determine P(person at any particular age will
live to a specified number of years)
Insurance Companies use these probabilities to
determine
STA 215
Professor Ochs
Problem Set #1
Due at Start of Class: 3 Feb 2015
WHERE APPROPRIATE YOU MUST SHOW YOUR WORK, ONLY PRESENTING FINAL
ANSWERS IS NOT NOW NOR
1
Problem to Turn In
1) First create the contingency table. The rows or columns may be reversed in your version, but I will use the
afliation as rows and the choice as columns.
Democrats
Republicans
I
High-powered hurricanes are known as major hurricanes, with categories 3, 4, or 5.
From the data below which counts major hurricanes in the decade ending on the
given
Ch 13 (Conditional Probability and the Bayes Theorem)
Recall:
10% of $254 = $25.4 (tax in an Asian/European country)
7% of $254 = $17.78 (USA tax)
Example 1
In a specific city, about 1% of drivers dri
Ch 18 (t-test)
Get Satistica ready. We will do things like the following:
t-test =
n
Two-tail
Probability
(by A-68 t-table)
Two-tail
Probability
(by Statistica)
observedexpected
. Assume t-test = 3.07
Chapter 3 Trim (Mean, Standard Deviation, and Quartiles)
n
x
=
1
x
n 1 i
n
p. 57:
x
1
x = 1 ( x + x + + x n ) .
n 1 i n 1 2
is called the mean of the data set.
Example 1:
(a) Incomes of 10 families i
Lecture 2
Ex. 1
In 1975, at U.C. Berkeley, the Dean of Graduate School noticed that about
45% of male applicants were admitted and about 30% of female applicants
got in. The difference was about 15%.
STA 215
Professor Ochs
Problem Set #5
Due at Start of Class: 13 Mar 2015
WHERE APPROPRIATE YOU MUST SHOW YOUR WORK, ONLY PRESENTING FINAL
ANSWERS IS NOT NOW NOR
STA215: Statistical Inference
Section 3, 4
Course Syllabus
Textbook: DeVeaux, Welleman, Bock: Intro Stats, 4th Ed.
Policy on Older Editions: Students may use earlier v
STA 215
Professor Ochs
Problem Set #4
Due at Start of Class: 27 Feb 2015
WHERE APPROPRIATE YOU MUST SHOW YOUR WORK, ONLY PRESENTING FINAL
ANSWERS IS NOT NOW NOR
STA 215
Professor Ochs
Problem Set #3
Due at Start of Class: 20 Feb 2015
WHERE APPROPRIATE YOU MUST SHOW YOUR WORK, ONLY PRESENTING FINAL
ANSWERS IS NOT NOW NOR
STA 215
Professor Ochs
Problem Set #2
Due at Start of Class: 10 Feb 2015
WHERE APPROPRIATE YOU MUST SHOW YOUR WORK, ONLY PRESENTING FINAL
ANSWERS IS NOT NOW NOR
1
Problem to Turn In
a) (dice) = 43 = 64
b) The minimum value will occur when each die shows its minimum, 1 + 1 + 2 = 4, and the maximum value when
each die has its maximum, 7 + 7 + 8 = 22. The full s
Sampling and Variables
Does varying one or more Explanatory
Variables (Independent Variables/Factors) have
an effect on a Response Variable (Dependent
Variable)
o Does varying the explanatory variable
Estimation & the t Distribution
Let be some number between 0 and 1.
1 is the confidence level
Z = the z-score that has area to its RIGHT
under the standard normal curve
Z.05 = the z-score that has ar
STA 115
Total points: 35
Quiz#1
NAME:
1. Identify the variable as Quantitative or categorical and state one possible graphical
method to display the distribution of this variable. [4]
Quant/Cat/Border
t Interval
o Draw an SRS of size n from a population having unknown mean . A level C confident
interval for is
o
is considered the upper critical value for the t(n 1) distribution
is found in Table
Calculating the z Test Statistic
o To test the hypothesis based on an SRS of size n from the a population with unknown
mean and known standard deviation , the z test statistic is
P-Value
o The probab
Proportions Review
Sample Proportions
o Tests and confidence intervals for a population proportion p when the data are an SRS
of size n are based on the sample proportion . When n is large, has approx