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Agenda of Week V Review of Week IV Inference on MV Mean Vector One population Two populations Multi-populations: MANOVA
Review of Week IV Random vector L.C. of random variables Multivariate normal distribution
Inference on MV Mean Vector Small sample case One population case
Inference on MV Mean Vector Large sample case
Inference on MV Mean Vector Confidence interval Small sample Large sample
Inference on MV Mean Vector Small sample case Two population case
Inference on MV Mean Vector Small sample case
Inference on MV Mean Vector Large sample case
MANOVA One-way MANOVA model Variation decomposition Total variation (T) df= N-1 Variation between Factors (B) df= k-1 Variation within Factors (W) df= N-k
MANOVA Wilks Lambda Distribution: When N is sufficiently large
1 Confidence Intervals for Means. 2 When the sample size n< 30 case1-1. the underlying distribution is normal with known variance case1-2. the underlying.
Normal Distribution. Confidence Interval 90% Level of Significance 10%
Agenda of Week VII Review of Week VI Multiple regression Canonical correlation.
Inference about Means/Averages Chapter 23 Looking at means rather than percentages.
Mean for sample of n=10 n = 10: t = 1.361df = 9Critical value = Conclusion: accept the null hypothesis; no difference between this sample.
1 Inference About a Population Variance Sometimes we are interested in making inference about the variability of processes. Examples: –Investors use variance.
Population Proportion The fraction of values in a population which have a specific attribute p = Population proportion X = Number of items having the attribute.
1 (Student’s) T Distribution. 2 Z vs. T Many applications involve making conclusions about an unknown mean . Because a second unknown, , is present,
Week 111 Review - Sum of Normal Random Variables The weighted sum of two independent normally distributed random variables has a normal distribution. Example.
Jump to first page STATISTICAL INFERENCE Statistical Inference uses sample data and statistical procedures to: n Estimate population parameters; or n Test.
: An alternative representation of level of significance. - normal distribution applies. - α level of significance (e.g. 5% in two tails) determines the.
1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Chapter 11 Inferences About Population Variances n Inference about a Population Variance n.
Horng-Chyi HorngStatistics II_Five43 Inference on the Variances of Two Normal Population &5-5 (&9-5)
Chapter 14 Single-Population Estimation. Population Statistics Population Statistics: , usually unknown Using Sample Statistics to estimate population.
Discriminant Analysis Objective Classify sample objects into two or more groups on the basis of a priori information.
Section 6.4 Inferences for Variances. Chi-square probability densities.
CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Confidence intervals.
SWBAT: -Interpret the t-distribution and use a t- distribution table -Construct a confidence interval when n<30, the population is normally distributed,
Section 7.5 Estimating a Population Variance. Symbol Check = population standard deviation = sample standard deviation = population mean = sample mean.
Multivariate Analysis of Variance, Part 1 BMTRY 726.
Confidence Intervals for a Population Mean, Standard Deviation Unknown.
AP STATISTICS LESSON COMPARING TWO PROPORTIONS.
Confidence intervals. Population mean Assumption: sample from normal distribution.
INFERENCE Farrokh Alemi Ph.D.. Point Estimates Point Estimates Vary.
Sampling Distributions A statistic is random in value … it changes from sample to sample. The probability distribution of a statistic is called a sampling.
1 Confidence Interval for a Mean. 2 Given A random sample of size n from a Normal population or a non Normal population where n is sufficiently large.
Agenda of Week VII. Sampling Distribution Objective : Understanding the standard normal distribution Understanding the sampling distribution Week 6 1 Random.
1 Chapter 12 Inferences for Population Proportions.
Inference ConceptsSlide #1 1-sample Z-test H o : = o (where o = specific value) Statistic: Test Statistic: Assume: – is known – n is “large” (so.
Chapter 9 Inferences Based on Two Samples: Confidence Intervals and Tests of Hypothesis.
Chapter 12 Inference for Proportions AP Statistics 12.2 – Comparing Two Population Proportions.
Chapter 7 Estimation. Chapter 7 ESTIMATION What if it is impossible or impractical to use a large sample? Apply the Student ’ s t distribution.
MathematicalMarketing Slide 4b.1 Distributions Chapter 4: Part b – The Multivariate Normal Distribution We will be discussing The Multivariate Normal.
1 BA 275 Quantitative Business Methods Quiz #2 Sampling Distribution of a Statistic Statistical Inference: Confidence Interval Estimation Introduction.
Comparing Means: Independent-samples t-test Lesson 13 Population APopulation B Sample 1Sample 2 OR.
Introduction to Inference Confidence Intervals Issue of accuracy Remember: all 3 conditions must be met (randomization, normality, independence) Margin.
MANOVA Multivariate Analysis of Variance. One way Multivariate Analysis of Variance (MANOVA) Comparing k p-variate Normal Populations.
Confidence Intervals for Means. point estimate – using a single value (or point) to approximate a population parameter. –the sample mean is the best point.
Estimating a Population Mean. Student’s t-Distribution.
Statistics for Business and Economics 8 th Edition Chapter 7 Estimation: Single Population Copyright © 2013 Pearson Education, Inc. Publishing as Prentice.
1 A heart fills with loving kindness is a likeable person indeed.
7.2 Confidence Intervals When SD is unknown. The value of , when it is not known, must be estimated by using s, the standard deviation of the sample.
Introduction to Inference Tests of Significance. Wording of conclusion revisit If I believe the statistic is just too extreme and unusual (P-value <
11 Comparison of Several Multivariate Means Shyh-Kang Jeng Department of Electrical Engineering/ Graduate Institute of Communication/ Graduate Institute.
Probability in Sampling. Key Concepts l Statistical terms in sampling l Sampling error l The sampling distribution.
Pg. 525 #13: A milk processor monitors the number of bacteria per milliliter in raw milk received at the factory. A random sample of 10 one-milliliter.
Confidence Intervals for Variance and Standard Deviation.
Decision making for two samples Inference about two population means.
1 1 Slide IS 310 – Business Statistics IS 310 Business Statistics CSU Long Beach.
Hypothesis testing –Revisited A method for deciding whether the sample that you are looking at has been changed by some type of treatment (Independent.
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