This version was posted after class. WEEK 7 Wed, Oct 13
Chapter 3. Random Variables and Probability Distributions on the Line. Discrete Probability mass function. p(x) Cumulative distribution function. F ( x) P( X x)
p( y )
y x
Expectation. value of X.
Statistics Tutorial: Power of a Hypothesis Test
The probability of not committing a Type II error is called the power of a hypothesis test.
Effect Size
To compute the power of the test, one offers an alternative view about the "true" value of the populati
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STT 315 (Secs 12 ~ 22) Final Exam - FORM D' 4-: 14/ l ed, Dec 15, 2010 '
Gilliland (Closed book - 120 minutes) ' same. 10:00 am - Noon
Name _ P11) 7 I TA
0. You may use a ealeulator. All electronic devices capable of commun
12/1/10 Posted before class.
EXAMPLE INVESTIGATION of COVERAGE PROBABILITY
Application to Auditing 1. INTRODUCTION. Suppose that over the course of three years, a medical care provider has submitted N = 200,000 bills for reimbursement under the government
WEEK 1 Sept 1 Go over Syllabus. Go over Tentative Schedule. Expected Coverage for Today. Ideas in Chapter 2, Sections 2-1 through 2-4. Types of probability: objective and subjective Probability models are used to mathematically model situations whe re out
WEEK 2 Wed, Sept 8 Expected New Coverage for Today. Ideas in Chapter 2, Sections 2-4 and 2-5. Example 1. Rolling Two Balanced Dice. For purposes of enumerating outcomes, think of one die as green in color and the other as red in color. We take S to consis
WEEK 3 Wed, Sept 15
Today: Cover Sections 2-7 and 2-8. Section 2-7. BAYES CALCULATIONS. We start with an informal approach. Example 1. (a) The prevalence of a disease is 5% in a population of 1,000 individuals. A person is selected at random from the popu
WEEK 4, Monday, Sept 20
Today: Cover Sections 3-1 through 3-3. Discuss discrete and continuous random variables and their distributions as probability models. Outcomes are on the real number line, often the events of interest are intervals. Discrete Proba
WEEK 4, Wednesday, Sept 22
Today: Cover Sections 3-3, 3-4, 3-5, and start 3-7.
Some Properties of Expectation and of Variance (Sec 3-3). For constants a and b,
E (aX b) aE( X ) b a b
(3-6) (3-10)
V (aX b) a 2V ( X ) a 2 2
Example 1. Profit from Products S
WEEK 5, Monday, Sept 27
Today: Cover Sections 3-8, 3-10 and 3-11.
Hypergeometric Distributions (Sec 3-8). The Hypergeometric probability distributions arise when counting Successes when sampling n at random from a dichotomous, finite population. Hypergeom
WEEK 5, Wednesday, Sept 29
Today: Cover material from Sections 3-12, 4-1, 4-2, 4-3, and 4-4. Exponential Distribution with Parameter > 0 (Sec 3-12). Here is the density function:
f ( x)
e x ,
x0 x<0
0, Graph the density function.
Important Results for E
WEEK 6, Monday, Oct 4
Today: Cover Sections 4-5, 4-7. Finding percentiles of Normal Distributions (Chap 4, Sec 4-5). TI-83. Use invNorm(.90, ) and get 90th percentile of the Normal distribution N( ). , , Excel. Use = norminv(.90, ) and get 90th percentile
Posted before class will be revised and re-posted after class
WEEK 6, Wednesday, Oct 6
Today: Cover some material from Sections 5-1, 5-2, 5-3. Sec 5-1. Discuss and motivate the use of data gathered in simple random samples for inferences about the populat
WEEK 8 Wed, Oct 20
DESCRIPTIVE STATISTICS and GRAPHICAL DISPLAYS
(Background material is in Chapter 1)
Overview of Data Types and Data Collection (Chap 1, Sec 1)
Measurement processes applied to subjects or entities produce data. Usually many variables ar
Posted before class
WEEK 9 Mon, Oct 25
GRAPHICAL DISPLAYS
(Background material is in Chapter 1)
Numerical Data Distributions Shapes of Distributions (Chap 1, Sec 5)
Discuss Skewness only, not Kurtosis. Delay discussion until after we have covered graphica
Posted before class
WEEK 9 Wed, Oct 27 Review of Sampling Distributions
RANDOM SAMPLING, SAMPLE STATISTICS, SAMPLING DISTRIBUTION
(Background material is in Chapter 5)
Sampling Distributions of Sample Statistics (Chap 5, Sec 3)
Henceforth, unless otherwis
Posted before class
WEEK 10 Mon, Nov 1
Large Sample CI for p (Chap 6, Sec 4)
Dichotomous Population. The point estimate of p is the sample proportion p . Ignoring the fpcf, a large n, (1 )100% confidence interval estimator (CI) for p is
p z / 2
p(1 p)
Posted before class
WEEK 10 Wed, Nov 3
Correct Formulas for Sample-Size Determination
The equations that should be solved when using simple random sampling from a population of size N are
B z / 2
N n N 1 n
(*)
B z / 2
with results
N n N 1
p(1 p) n
(*)
2 z
Posted before class
WEEK 11 Mon, Nov 8
Lower Estimates - (1 )100% Confidence Level One-Sided Confidence Intervals
Guidelines from the Centers for Medicare & Medicaid Services state In most situations, the lower limit of a one-sided 90 percent confidence i
Posted before class
WEEK 11 Wed, Nov 10
HYPOTHESIS TESTING The p-value Approach
(Background material is in Chapter 7)
Conventions in Hypothesis Testing: 1. One usually selects as the null hypothesis, the hypothesis that we will retain (live with) unless t
Posted before class
WEEK 12 Mon, Nov 15
HYPOTHESIS TESTING The p-value Approach
(Background material is in Chapter 7)
Tests for Mean ; the p-value Approach
Population Standard Deviation Known - a z-test. The test statistic is which when standardized relat
Posted after class
WEEK 12 Wed, Nov 17
REVIEW UNIT 2
Chapter 1
Describing Data Sets - Chap 1: Secs 1, 2, 3, 4, 5, 9
Measurement processes applied to subjects or entities produce data. Usually many variables are measured for which data are recorded. You mu
Posted after class.
WEEK 14 Mon, Nov 29
HYPOTHESIS TESTING Critical Value Approach
(Background material is in Chapter 7)
Tests for Mean
Population Standard Deviation Known - a z-test.
is The test statistic
where or The textbook ignores the size of the po
Posted before class.
WEEK 14 Wed, Dec 1
HYPOTHESIS TESTING Prof. Thomas Page Approach
Last time we went through the example MC problems 7 9 toward the end of the list of MC problems. We went through Professor Thomas Pages Six Steps. Step 1 involves settin