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# Exam 3 study guide STAT 200

Penn State

GPA 3.59

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## Popular in Elementary Statistics

## Popular in Statistics

This 5 page Study Guide was uploaded by Kelsey Marr on Monday April 20, 2015. The Study Guide belongs to STAT 200 at Pennsylvania State University taught by Andrew Wiesner in Winter2015. Since its upload, it has received 292 views. For similar materials see Elementary Statistics in Statistics at Pennsylvania State University.

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Date Created: 04/20/15

Stat 200 Andrew Wiesner Exam 3 Study Guide Chapter 7 Hypothesis or Signi cance Testing 0 5 steps to testing 0 set up 2 competing hypotheses One is the null and one is the alternative 0 Set some level of signi cance called alpha for class purposes it will be 005 0 Gather data and calculate a test statistic 0 Calculate the probability value called pvalue associated with the test statistic amp using the alternative to guide us P value probability our sample would produce the result assuming null is true 0 Compare pvalue to alpha and make a decision to either reject the null or fail to reject the null Chapter 8 Comparing Two Groups 0 Sampling Distribution for Difference in 2 Sample Proportions 0 Used when 2 populations are formed by a categorical variable and a comparison of some feature of the two populations is wanted 0 Estimate the value of the difference in 2 population proportions 0 Test the hypothesis that the difference between 2 population proportions is 0 If the difference is 0 the 2 proportions are equal 0 Conditions Must be 2 independent samples randomly selected from the 2 populations n1p1 n11p1 n2p2 and n21p2 must be at least 10 0 Con dence Intervals for difference between population proportions 0 Used when there are 2 populations from which independent samples are available 0 Conditions Sample proportions must be independent or randomly selected n1phat1 n11phat1 n2phat2 and n21phat2 must be at least 10 0 Sample distributions for sample mean of paired differences 0 Matched pairs 2 measurements from the same individual measured under conditions or at 2 different times Dependent samples data collected as matched pairs because the 2 observations are not statistically independent of each other Conditions Population must be bell shaped and a random sample OR Population of interest has a large random sample n is greater than or equal to 30 Paired data data that have been obsereved in natural pairs Use paired data to allow you to get rid of variation from pair to pair so you can observe variation between methods Interpreting CI for the mean of paired differences If Cl does include 0 it is possible that the population means for the 2 measurements could be the same If Cl does not include 0 fairly certain that the population means for 2 variables are different 0 Sampling Distribution for the Difference in 2 Sample Means 0 Independent sample individuals in one sample aren t coupled in any way with individuals in other sample 0 CI for Difference in 2 Population Means 0 Compare means of a quantitative variable for the two populations or for the two groups within a population 0 2 Sample 2test t sample statistic null value standard error 0 Equal variance assumption 0 O Pooledpooling variance If the variance of the 2 independent groups be it proportions or means we can strengthen our test by pooling the variances into one vanance The choice to pool or not to pool is an option in the software with default being not to pool We will pool the two proportion variances if the value in our hypothesis to test is 0 For 2 indpendent means we will pool the variance if ratio of largest SD smallest SD is less than or equal to 2 Chapter 9 Analysis of Variance ANOVA We use this method to compare more than 2 independent means 0 Primary concerns 0 0 Setting up correct hypothesis Determining correct degrees of freedom and using this info to establish how many means are being compared and what the total sample size is 0 Checking assumptions Normality Equalvanance 0 Determining which group mean or means differ when we reject the null hypothesis Hypothesis 0 Ho all means are equal or all group means are equal 0 Ho m1m2m3 0 Ha not all group means are equal 0 Ha at least 1 mean differs The test for ANOVA uses an Fstatistic or Ftest This f statistic is a ratio of between group variance to within group variance 0 The between group variance is a measure of difference between each group mean and the overall mean Between group DF l numerator DF g1 o The within is a measure of the difference between each observation and its group mean Within group DF l denominator DF ng f stat between group variance within group variance The pvalue given from the software is the probability of getting this f statistic or one more extreme Chapter 10 Categorical Data Categorical variables are raw data made up of group or category names that don t necessarily have a logical order Contingency tables are used to display all possible combinations of 2 categorical variables Row category is typically the explanatory variable Column category is typically the response variable Inferential statistics 0 When sample evidence is used to infer something about the entire population 0 Statistically signi cant relationship It can be inferred that a relationship exists in the population 5 steps to determining statistical signi cance 0 determine null and alternative hypotheses o summarize data into the appropriate test statistic after rst verifying that necessary data conditions are met 0 Find the pvalue of the chisquared statistic 0 Using the pvalue determine whether the result is statistically signi cant 0 Come up with a conclusion based on your ndings in the previous steps Calculating the chi squared statistic o Xquot2 the summation of observed count expected countquot2 expected count Factors that affect statistical signi cance 0 As the difference in row percents increases chi square increases and pvalue decreases 0 As n increases chi square increases and pvalue decreases Risk and Relative Risk 0 Risk number in category total number in group 0 Relative risk risk in category 1 risk in category 2 0 Odds compare the chance of an event happening to the chance of an event not happening for a group Confounding variable 0 A variable that effects the response variable and is also related to the explanatory variable lurking variable 0 a term used to describe a potential confounding variable that is not measured and is not considered in the interpretation of a study Chapter 11 Correlation and Regression Scatterplots 2D graph of the measurements for 2 numerical variables 0 Explanatory variable x variable 0 Dependent variable y variable Regression equation Yhat bo b1x Intercept coefficient bo Slope coefficient b1 Simple linear regression analysis where you attempt to nd the line that best estimates the relationship between two variables 0 Regression anaylsis used to examine the relationship between a quantative response variable and one or more explanatory variables Deterministic relationship a relationship where if we know the value of one variable we know exactly the value of the other variable Statistical relationship there is variation from the average pattern 0 Most relationships are statistical Prediction error the difference between the observed value of y and the predicted value of yhat for an observed value of x 0000 0 Correlation o A number used to indicate the strength and direction of a straight line relationship Strength of relationship closeness of points to a straight line Direction of relationship indicates whether one variable generally increases or decreases as the other variable increases

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