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# Class Notes for Statistics at University of Michigan - Ann Arbor

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##### STATS 250 Lecture Notes - Lecture 41: Null Hypothesis 24HRPremium

I. Test of Independence A. Helps us to assess if two discrete (categorical) variables are independent for a population, or if there is an association between the two variables B. Example 1. Scenario: We have one population...

Statistics
STATS 250
##### STATS 250 Lecture Notes - Lecture 40: Null Hypothesis 24HRPremium

I. Test of Homogeneity A. Helps us to assess if the distribution for one discrete (categorical) variable is the same for two or more populations B. Example 1 1. Scenario: We have two populations of interest; children and a...

Statistics
STATS 250
##### STATS 250 Lecture Notes - Lecture 39: Count Data, Test Statistic, Null Hypothesis 24HRPremium

I. Chi-Square Analysis A. Inference for Categorical Variables 1. Goodness of Fit Test = Assessing if a particular discrete model is a good fitting model for a discrete char...

Statistics
STATS 250
##### STATS 250 Lecture Notes - Lecture 38: Regression Analysis, Scatter Plot, Test Statistic 24HRPremium

I. Correlation and Linear Regression A. Example 1. Relationship between Time at Preschool and Language Development Does a childs language development depend on the amount of tie the child spends in preschool. A recent stud...

Statistics
STATS 250
##### STATS 250 Lecture Notes - Lecture 37: Prediction Interval, Standard Deviation, Confidence Interval 24HRPremium

I. Correlation and Linear Regression A. Predicting for Individuals versus Estimating the Mean 1. Consider the relationship between the apartment size and monthly rent price a) = 227.8705 + 0.8303x 2. We also have : s = 126...

Statistics
STATS 250
##### STATS 250 Lecture Notes - Lecture 36: Dependent And Independent Variables, Total Variation, Normal Distribution 24HRPremium

I. Correlation and Regression Analysis A. Describing a Linear Relationship with a Regression Line 1. The simplest kind of relationship between two variables is a straight line, the analysis in this case is called linear re...

Statistics
STATS 250
##### STATS 250 Lecture Notes - Lecture 33: Dependent And Independent Variables, Confidence Interval, Total Variation 24HRPremium

I. Modeling Relationships (Regression) A. To be able to perform the pooled two-sample t test (or confidence interval)... 1. The needed assumptions is that the population standard deviations are equal 2. And we check the as...

Statistics
STATS 250
##### STATS 250 Lecture Notes - Lecture 31: Analysis Of Variance, Confidence Interval 24HRPremium

I. ANOVA Example A. Memory Experiment 1. In a memory experiment, three groups of subjects were given a list of words to try to remember. The length of the list for the first ...

Statistics
STATS 250
##### STATS 250 Lecture Notes - Lecture 30: Standard Deviation, Coaltar Of The Deepers, Test Statistic 24HRPremium

I. Analysis of Variance A. Examples 1. Comparing 3 Drugs We wish to compare three drugs for treating some disease. A quantitative response (time to cure in days, also called recover time) is measure such that a smaller val...

Statistics
STATS 250
##### STATS 250 Lecture Notes - Lecture 29: Analysis Of Variance, Null Hypothesis 24HRPremium

I. Analysis of Variance (ANOVA) - allows us to compare means of two or more normal populations based on Independent random samples when population variances are assumed to be Equal - an extension of the two independent sam...

Statistics
STATS 250
##### STATS 250 Lecture Notes - Lecture 28: Beta Blocker, Normal Distribution 24HRPremium

I. Testing About a Difference in Population Means A. Testing Hypotheses About the Difference in Two Population Means 1. Assumptions a) Independent random samples b) Come from Normal population (but if sample size is large,...

Statistics
STATS 250
##### STATS 250 Lecture Notes - Lecture 27: Confidence Interval, Silent Generation 24HRPremium

I. Confidence Interval for the Difference in Two Population Means A. Examples 1. On-Demand Viewing 1:Population mean amount of time (minutes) spent watching on demand TV by...

Statistics
STATS 250
##### STATS 250 Lecture Notes - Lecture 26: Dependent And Independent Variables, Confidence Interval 24HRPremium

I. Learning About the Difference in Population Means A. The Independent Samples Scenario 1. Random samples are taken separately from two populations and the same response variable is recorded for each individual 2. Partici...

Statistics
STATS 250
##### STATS 250 Lecture 25: Learning About a Population Mean Difference 24HRPremium

I. Confidence Interval for a Population Mean of Paired Differences A. Examples 1. Changes in Reasoning Scores Do piano lessons improve spatial-temporal reasoning of preschool ...

Statistics
STATS 250
##### STATS 250 Lecture Notes - Lecture 24: Confidence Interval, Standard Deviation, Type I And Type Ii Errors 24HRPremium

I. Testing About a Population Mean A. Examples 1. Time Spent Watching TV A study looked at the amount of time that teenagers are spending watching TV. Based on a representative sample, the 95 confidence interval for mean a...

Statistics
STATS 250
##### Statistics - Reference Guides

This Guide provides an easy to follow summary of all basic principles that are the foundation to Statistics and Probabilities. Using a combination of charts and sample equations, the key concepts are developed and the esse...

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