Statistics 285
Solutions to HW #1 Problems
1.14
a.
The two variables measured are type of credit card used and amount of purchase.
Type of credit card used is qualitative. It has no meaningful number associated
with it, only the name of the card used. Amo
Section 2.3- 2.7
Center
Spread
Calculating median, m
Arrange the n measurements from smallest to largest
1. If n is odd m is the middle number
2. If n is even m is the mean of the middle two numbers
Skewed dataMedian <Mean- Rightward skewness
Mean=Median
Syllabus Stat 285 Spring 2011 A. Course: 960:285:01, Statistics for Business- Section 01 B. Prerequisites: 01:640:115 or equivalent. Credit not given for more than one of 01:960:201, 211, 285, and 401. C. Meeting Times: Tuesday/Thursdays 2:50-4:10 PM D. L
Stat 960:285
Assignment #4
Due Date 3/1/2012
Problem 1
An urn contains two green balls and three red balls. Other than color the balls are
identical, thus the chances of picking each ball is equally likely. Suppose two balls will be
drawn at random one af
Stat 960:285
Assignment #6
Due Date 3/20/2012
Find the following probabilities. It helps to sketch the p.d.f. for Standard Normal Distribution
and shade in the area that corresponds to the probability of interest.
Grading: If they have the wrong answer an
Stat 960:285
Assignment #5
Due Date 3/8/2012
For all of these problems, remember the fact that random variables taking on specific values is an
event, thus they can be manipulated using unions, intersection, complements and set deletions.
Consequently, th
Stat 960:285
Assignment #7
Due Date 4/5/2012
Part I
Problem #1
The weights of the drained fruit found in 21 randomly selected cans of peaches packed by Sunny
Fruit Company were (in ounces)
11.0
11.6
11.6
10.9
11.7
12.0
11.6
11.5
11.2
12.0
12.0
11.2
11.4
1
Bad Statistical
Practice
Practice
By: Andrew Magyar
Association and Causality
No matter what the nature of the data, even if
there does seem to be a relationship between the
two variables, one must not be too hasty in
concluding that the nature of the re
Bivariate
Bivariate Data - I
By: Andrew Magyar
Bivariate Data
Up to now, dealt with data in which there was
only one variable we were interested in.
In other words there was exactly one data point
for each experimental unit.
Many interesting problems i
Bivariate
Bivariate Data - II
By: Andrew Magyar
Quantitative &
Qualitative
Qualitative
Example 2: Cancer Survival Data
Patients with advanced cancers of the
stomach, bronchus, colon, ovary or breast
were treated with ascorbate. The purpose of
the study w
Descriptive Statistics for
Quantitative
Quantitative Data - I
By: Andrew Magyar
Notation
Suppose we have n experimental units and are
interested in a single variables that is
quantitative in nature.
Let xi denote the value of the variable for the ith
ex
Graphical Displays
for
for Qualitative Data
By: Andrew Magyar
Charts and Displays for Nominal Data
Example 1: Suppose we sampled 10 clients
from a local travel agency and asked them
their travel destination for their upcoming
summer
summer vacation. Belo
When to add and when to multiply?
Calculating probabilities for experiments involving multiple elements may be a little confusing when should you add and when should you multiply two probabilities to get a final probability
for an outcome/event? The basic
Stat 960:285
Assignment #3
Due Date 2/23/2012
Question 1
Part I - Shade in the area on a Venn diagram that represents the events listed in (a) through (j).
You will have to draw a separate Venn diagram for each event.
For events A and B, start with the fo
Statistics 285
Solutions to HW #5 Problems
6.12
Let p = proportion of U.S. companies that have formal, written travel and
entertainment policies for their employees. The null hypothesis would be:
H0: p = .80
6.13
Let = mean caloric content of Virginia sch
Confidence Interval for Population Mean
For Single Sample Experiments
Sample Size
Distribution of x
Normal with
s
x =
n
Population is not
Normal (deviates from
Normal significantly)
or of unknown
distribution
Small (n < 30)
Normal with
x =
n
Population is
Statistics 285
Solutions to HW #4 Problems
5.8
a.
For confidence coefficient .95, = .05 and /2 = .05/2 = .025. From Table
IV, Appendix B, z.025 = 1.96. The confidence interval is:
x
b.
x
s
3.3
z.025 n 33.9 1.96 100 33.9 .647 (33.253, 34.547)
s
z.025
n
3
Stat 960:285
Assignment #1
Due Date 2/2/2012
Instructions:
1) Write your name & the section number that you are registered for on your
submission.
2) Include all relevant computer output and code. Do not print out the data. For
instance, if you use Excel,
Hypothesis Tests & Confidence Intervals for a population
proportion p
Suppose the data X1, . . ., Xn is an i.i.d. sample with Xi ~ Bern(p)
It follows for large n,
p (1 p )
1n
p = X i ~ Norm p,
n i =1
n
a) Two-sided Hypothesis Test (Test for Equality)
H0
Introduction
Introduction
By: Andrew Magyar
What is Statistics?
Most people view statistics merely as collecting,
organizing, and presenting figures and numbers.
This is only part of what statistics is about.
Wiki-definition: the formal science of maki
Stats: Correlation & Regression
Definitions
Coefficient of Determination
The percent of the variation that can be explained by the regression equation
Correlation
A method used to determine if a relationship between variables exists
Correlation Coefficien
Stats: Estimation
Definitions
Confidence Interval
An interval estimate with a specific level of confidence
Confidence Level
The percent of the time the true mean will lie in the interval estimate given.
Consistent Estimator
An estimator which gets closer
Stat 960:285
Assignment #9
Due Date 4/12/2012
Problem #1
A sample of 12 radon detectors of a certain type was selected, and each was exposed to
100 pCi/L of radon. The resulting readings were
105.6 90.9
91.2
96.9
96.5
91.3
100.1 105.0 99.6
107.7 103.3 92.
Introduction to
Inferential
Inferential Statistics
By: Andrew Magyar
Essentially, all models are wrong, but some are
useful
useful.
Statistician George Edward Pelham Box
All sciences make assumptions that phenomena of
interest
interest behaves like som
MID-TERM II Introductory Statistics for Business 01:960:285
NAME: _
Section: _
Instructions:
a) Read the Instructions.
b) Put your name and section number on the Mid-Term sheet.
c) You are allowed only one 8.511 sheet of notes and a calculator.
d) Show an
Appendix B Tables 1143
TABLE II Binomial Probabilities
p ( x)
012345678910
k
Tabulated values are 2p(x). (Computations are rounded at the third decimal place.)
1:0
I7
k .01 .05 .10
.951 .774 .590 .328 .168 .078 .031
.999 .977 .919 .737 .528 .337 .18
Summary of Discrete Probability Distributions
Description
Examples
Experiments involving only two
outcomes. Example: Flipping a coin and
counting number of Heads (X), i.e.
successes, in a fixed number of trials
(n). On any trial, the probability of
succes
Confidence Interval for Population Mean
For Single Sample Experiments
Sample Size
Large (n 30)
Population
distribution &
whether is known
Population is Normal
(or approx. Normal)
and is known
Population is Normal
(or approx. Normal)
and is unknown
Populat
Statistical Hypothesis Tests (Chapter 7)
Rejection Regions for Typical Values of
(Large Samples, i.e., n 30)
Alternative Hypotheses
One-lowertailed test
One-uppertailed test
Two-tailed test
0.10
z < -1.282
z > 1.282
z < -1.645 or z >1.645
0.05
z < -1.645