STAT 200 Exam 4 Study Guide s Sample Standard Deviation Sample Mean Population Mean Population Standard Deviation Symbols Graphs Review of Previous Material 1 Standard Deviation Scatterplot Two Quantitative Variables Two Dimensional Bar Graph Two Categorical variables displayed on 2x2 contingency table Bar Graph One Categorical Variable Histogram One Quantitative Side By Side Boxplot Individual Value Plots One Quantitative Response Variable One Categorical Explanatory Variable Two Independent Samples Line Plot One Quantitative Response Variable One Categorical Explanatory Variable Two Dependent Samples a Requires a normal shape b Can only be interpreted when considering the sample mean c Sensitive measure of spread d Roughly defined as the average distance of an observed value from the mean e Only fully interpreted when empirical rule is applied 2 Correlation vs Regression a Correlation i Strength and direction of how close the observations are to the potential straight line ii Sensitive Measure iii Only compare to correlations of same sample size iv Increases or decreases in strength when outlier is present v Stripped of original units of measurement found with the 2 variables vi Don t need to identify explanatory and response variables vii Possible Values 1 to 1 1 Strongest relationship 1 or 1 2 Weakest Relationship 0 b Regression i Used to find the best straight line to fit the data points ii Need to identify explanatory and response variables iii Method of least squares 1 Minimizes SSE iv Interpreting Slope on Regression Line 1 Example from Exam 2 a X time needed to complete paper hours Y length of paper pages Paper length 1 4 1 2 time in hours regression equation For Each additional hour the paper decreases by 1 4 pages in length v Regression Analysis Taken from Question on Exam 3 1 Goal is to minimize value of SSE when solving for the sample slope and sample y intercept 2 Underlying model requires that at each value of X there is a corresponding distribution for possible values for Y which are normal in shape and have the same variation 3 Population model for regression line is E Y 0 1X 4 The quantity of SSTO in the ANOVA table quantifies the amount of variation found with the response variable 3 Binomial Distribution a Two possible outcomes for each trial i Success fail b Original data is categorical c Random variable is discrete d Outcome for each trial are independent e Probability of success remains constant f Variable x is defined x number of successes g Possible values 0 to n h To find statistical inference i One sample sign procedure 4 Chi Square Distribution a Possible values 0 to b Is used with data summarized in 2x2 tables c Can t find exact probabilities d Continuous e Allows only for one sided hypothesis tests 5 Standard Normal Distribution a Continuous Distribution b Mean 0 c Standard deviation 1 6 t distribution a Continuous b Always bell shaped i Centered at 0 c Determined by degrees of freedom df n 1 i As degree of freedom increases distribution gets closer to standard normal curve d To find statistical inference i One sample t ii Two sample t iii Paired t a Continuous b Mostly between 3 to 3 c One and two sided d Can t find exact probabilities 7 Z Distribution i Can only find probabilities for a range of values e To find statistical inference i One proportion Z 1x2 table ii Two proportion Z 2x2 table 8 Confidence Interval a Intervals of values that researcher is fairly sure will cover the true unknown value of the population parameter b Used to estimate the value of a population parameter c The larger the n the greater the confidence interval 9 Confidence Interval vs Hypothesis Test a Confidence Interval clue words i by how much more ii estimate the population percent b Hypothesis Test clue words i if average differs from 10 Statistical Methods a Descriptive Method i Graphs ii Numbers b Inferential Method i Confidence Interval ii Hypothesis Tests p values New Material Chapter 11 Confidence Interval for Population Mean 1 Categorical Variables Proportions a One population proportion i P population parameter ii p sample statistic b Difference in 2 population proportions i p1 p2 population proportion ii p 1 p 2 sample statistic 2 Quantitative Variables Means a One population mean b Population mean of paired difference dependent i population parameter ii x sample statistic i d population proportion ii d sample statistic c Difference in 2 population means independent i 1 2 population proportion ii x 1 x 2 sample statistic a Measures average distance between statistic and parameter 3 Standard Error i s e x s n 4 INTERPRETATIONS a Standard Error for Mean i Over all samples of n the average distance between a sample mean and the true population is number from s n b Margin of Error c Confidence Interval i The difference between our sample mean of and the true population mean will be within i We are 95 confident that the population mean is between to 5 Confidence Interval for Population Mean a Formula i Sample estimate multiplier x standard error 6 t distribution vs z distribution a Similarities i Continuous ii Mean 0 iii Bell shaped b Use t distribution when i Data is quantitative ii Population standard deviation is unknown iii Estimating sample mean c Use z distribution when i Data is categorical ii Estimating sample proportion Chapter 12 Hypothesis Test for Population Mean 1 Hypothesis for Mean a Population mean 98 6 degrees i Ex determine whether the mean body temperature for humans is b Population mean difference for paired data d i Ex whether the mean difference in height between college men and their fathers is 0 son s height father s height c Difference between the means of two populations 1 2 i Ex Whether the mean time of television watching per week is the 2 Hypothesis Testing same for men and women a Also known as significance testing b Statistical significance is found and reject null if p value 05 c When referring to mean the null hypothesis will be the mean 3 t statistic test statistic a Standardized statistic used for hypotheses about means i for hypotheses about proportions the standardized statistic is called b Measures the distance between the sample statistic and the null value z statistic i t statistic equation 1 t sample statistic null null standard error c t distribution used to find the p value i standard normal distribution is used to find the p value d INTERPRETATIONS i Test Statistic ii P Value 1 Our sample mean of is t statistic equation