STAT 204 EXAM 2
6.1 6.4
Uniform Probability Distribution
Normal Probability Distribution
Standard normal probability distribution
Converting to the standard normal probability
distribution formula
Continuity correction factor
Exponential probability distr
Homework, Stat 204 (Exam 1)
Solutions to selected problems are located at the end of the document.
The problems assigned for each lab are due at the end of that lab meeting.
HW 1
1. Consider the data set for the sample of seven impact wrenches (caranddriv
STAT 204 Statistics for Business Students
Spring 2013
Location:
Tuesday and Thursday: Clark A104; Friday: (assigned lab room)
Instructor:
Dr. Mark Dahlke, Assistant Professor
104 Statistics Building
(970) 491-5330, mark.dahlke@colostate.edu
Office hours:
12/6/2011
I. Model assumptions
A. Mostly about error terms
B. Can look at residual plot here, too (residuals vs. )
II. Hypothesis tests (is it a good model?)
A. For overall significance, F
B. For individual significance, t
C. Ex.
MSE value is found under
11/29/2011
I. Cautions
A. Significant relationship doesnt imply cause-and-effect
B. Be careful about extrapolation
C. Be aware of influential points
D. A Large slope isnt always significant
II. ANOVA table
A. Convenient way to report information about SS
11/15/11
I. Sums of squares, SS
A. Explains the variation of the y-values; useful in formulas
B. Three types of SS
1. SSR= SS due to regression; 2. SSE= SS due to errors;
3. SST= SS total;
C. Overall relationship: SST= SSR+SSE
D. Want error to equal 0 and
8/23/11
Chapter 1
I. Data terminology
Elements
US Adults
Variable
Height
Gender
Type of Data
Numeric (Quantitative)
Categorical (Categorical)
NFL Teams
Wins
Points Scored
Payroll
Numeric
Numeric
Numeric
II. Goals
A. Summarize and describe lists of numbers
9/6/11
Probability Terminology
A. Experiment: Process that generates outcomes
Ex. Roll one die
B. Sample space: Set of all possible outcomes of an experiment
Ex. 1, 2, 3, 4, 5, 6
C. Event: Subset of the sample space
Ex. A = roll an odd number
B = roll a 5
8/30/11
I. Center
A. Location?
B. Two ways to measure location
1. Mean, uses more information
2. Median, not influenced by outliers
C. Ex. Football scores
Ordered data: 6 10 17 17 40 44 45 56
Index: 1 2 3 4 5 6 7 8
Mean: formula = xi/h
= 325/8 =29.4
Media
11/1/11
I. Why ANOVA?
A. Compare more than 2 population means?
k 3
B. General idea:
1. Assume is the same for each population
2. Estimate in two ways
a. MSTR (between treatments)
b. MSE (within [pooled] treatments)
3. Assume all population means are equal
11/8/11
I. Simple linear regression
A. Inference (two variables)
B. SLR model, y= (intercept)+(slope)x+ , assume a linear relationship between x and
y
C. SLR equation, E(y)= +x, unknown population parameters
D. Estimated SLR equation, = + x
1. Goal: find
9/27/2011
I. Terminology
A. Element, ex. Student
B. Population, ex. All CSU students
C. Sample, ex. Students in this class
D. Inferential statistics: use a sample to draw conclusions about a population
II. Selecting a sample
A. Important part of inferenti
9/20/2011
I. Continuous RVs
A. x and f(x)
1. too many xs to list
2. Draw the graph of f(x) to help you
B. Finding probabilities
1. Look at intervals of x values
2. The enclosed area on the graph is the probability
C. GRAPH
II. Normal RV
A. Very useful con
10/18/2011
I. Methods for testing hypothesis
A. p-value (most common)
B. CI (for 2-tailed)
C. Critical value
II. The p-value method
A. 5-step process
1. State the hypothesis
2. Specify (level of significance)
3. Compute the test statistic (from sample dat
10/4/2011
I. Estimation
A. Point= one number (best guess)
B. Interval= range of values near our point estimate
1. General form (pt. est.)(margin of error)
2. Include a probability statement
II. Confidence Interval (CI)
For ( unknown)
A. Uses the z distrib
10/25/11
I. Comparing two population means
A. Types of inference: CI and/or hypothesis test
B. 3 cases possible
1. , s known, independent samples (use z)
2. , s unknown, independent samples (use t)
3. = , matched pairs sample
II. Case 1
A. The hypothesize
9/12/2011
I. Binomial RV
A. RV, x= number of successes in n trials
B. How to recognize a binomial RV
1. n independent trials
2. Each trial= success or failure
3. Probability of success, p, is the same for each trial
C. Possible values for x= 0, 1, 2, 3n
D
10/11/11
I. Introduction/Review
Confidence Intervals
Mean ()
Proportion (p)
z ( known) t ( unknown)
z only
Hypothesis Tests
Mean ()
Proportion (p)
z ( known) t( unknown)
z only
II. Hypothesis Tests
A. Hypothesis: some conjecture about a population paramet
Month
OH Cost
MH
January
14,162
February
12,994
March
15,184
April
15,038
May
15,768
June
15,330
July
13,724
August
14,162
September
15,476
October
15,476
November
12,972
December
14,074
SUMMARY OUTPUT
20
20
21
22
22
21
19
21
22
23
18
21
# of units produc
2.1 2.2
Frequency Distribution
A frequency distribution is a tabular summary of data showing the
number (frequency) of items in each of several nonoverlapping
classes
Relative Frequency
= frequency of class/n
Histogram
Common graphical presentation of qua
# 19, pg. 353
In 2001, the U.S. Department of Labor reported the average hourly earnings for
U.S. production workers as $14.32 per hour (The World Almanac). A sample of
75 production workers during 2003 showed a sample mean of $14.68 per hour.
Assuming th
F Distribution
0
F
F -values for selected UPPER TAIL probabilities are shown in the following table:
Upper
tail
area
1
2
3
4
5
6
7
8
9
10
11
1
0.10
0.05
0.025
0.01
39.86
161.45
647.79
4052.18
49.50
199.50
799.50
4999.50
53.59
215.71
864.16
5403.35
55.83
2
t Distribution
0
t
t-values for selected UPPER TAIL probabilities are shown in the following table:
99%
For this CI
.01
.005
Upper tail probability
12.706
4.303
3.182
2.776
31.821
6.965
4.541
3.747
63.657
9.925
5.841
4.604
2.015
1.943
1.895
1.860
1.833
Standard Normal Distribution
z
0
Cumulative probabilities for NEGATIVE z-values are shown in the following table:
z
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
3.4
3.3
3.2
3.1
3.0
0.0003
0.0005
0.0007
0.0010
0.0013
0.0003
0.0005
0.0007
0.0009
0.0013
0.0003
0.
Homework, Stat 204 (Exam 3)
Solutions to selected problems are located at the end of the document.
The problems assigned for each lab are due at the end of that lab meeting.
HW 7
1. Consider the hypothesis test:
H0 : 60
Ha : < 60
Assume we have a sample o
Stat 204 Exam 3 review
* You WILL need a calculator for the test. *
1. A stockbroker believes the average number of shares (in millions) traded daily in the stock market is 500. To test the claim, he selects a random sample of 40 days and nds the mean num
Formulas: Stat 204 Exam 2 (updated Spring 2012)
x=
xi
n
IQR = Q3 Q1
(xi x)2
n 1
2
s=
(
=
x2
i
n 1
xi )2
n
Q1 1.5(IQR)
E (x) = =
i=
p
100 n
Q3 + 1.5(IQR)
xf (x)
V ar(x) = 2 =
(x )2 f (x) = (
x2 f (x) 2
x e
x!
n!
f (x) = x!(nx)! px (1 p)(nx)
f (x) =
E (x)
Stat 204 Exam 2 review
* You WILL need a calculator for the test. *
1. Use the standard normal distribution to nd the probability. P (2.56 < z < 0.37)
2. The average waiting time for a help desk call to be answered is 2 minutes. Assume the waiting
time fo