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# Midterm 2 Study Guide STAT 1350 Intro to Stats

OSU

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This 8 page Study Guide was uploaded by Katie Catipon on Thursday March 26, 2015. The Study Guide belongs to STAT 1350 Intro to Stats at Ohio State University taught by Alice Miller in Spring2015. Since its upload, it has received 547 views. For similar materials see Intro to Stats in Statistics at Ohio State University.

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Date Created: 03/26/15

Chapter 13 Normal Distributions Density curves Formed by smoothing out edges of a histogram Show the proportion of observations in any region by areas under the curve vs the counts of observations via heights amp areas of bars in a histogram Most useful for describing large numbers of observations 0 Choose a scale so that the total area under the curve exactly 1 0 Median of density curve divides the area under the curve into halves Quartiles dived the curve into quarters 0 Mean of density curve the point at which the curve would balance if made of solid material Symmetric curve this point is the center Mean of skewed distribution is pulled towards the long tail away from the median Note in a symmetric curve median and mean are the same value center Normal curves Symmetric mean amp median peak singlepeaked bellshaped Tails fall of quickly so do not expect outliers Described using mean u and standard deviation 0 0 Standard deviation eye of the curve Points at which curvature occurs located one standard deviation on either side of the meanmedian Mean xes center standard deviation xes shape l changing mean does not change shape only location on axis However changing standard deviation does change shape 6895997 Rule the quotEmpirical Rulequot in any normal distribution approx 0 68 of observations fall within 1 standard deviation of the mean 0 95 of observations fall within 2 standard deviations of the mean 0 997 of observations fall within three standard deviations of the mean 0 100 total are under the curve Standard scores 2 observations expressed in standard deviations above or below the mean of a distribution Zscore observation mean standard deviation Zscore translates directly into percentiles If you re looking for the percent of observations belowthe Zscore the answer the percentile If you re looking for the above the Zscore the answer 100the percentile Negative Zscore l percentile lt 50 Zscore zero l 50 0 Positive Zscore l percentile gt50 Solving Problems 0 Looking for a percent l forward problem To solve know observed value Calculate zscore Use table to convert into 0 Looking for observed values l backward problem To solve know Use table to convert to zscore Plug into equation to solve for observed value Chapter 14 Describing Relationships Scatterplots and Correlation Scatterplots most common way to display the relationship between two quantitative variables measured on the same individuals Each individual in the study appears as a point in the plot The point is determined by both variables for that one individual How to examine a scatterplot look for the overall pattern described by form direction and strength and striking deviations from the pattern outliers 0 Form linear Nonlinear No obvious pattern 0 Direction positive or negative No association 0 Strength strongmoderateweak pattern Linear straightline relations simple and common It is strong if the points all lie close to the line and weak if they are widely scattered about the line Association direction relationship between x and y causation Association As x explanatoryindependent variable increases so does y responsedependent variable The slope moves upwards from left to right 0 Association As x increases y decreases Plot slopes downward left to right Correlation r numerical description of the direction and strength of a linear relationship between x and yquotv v vv v unus lylv nili v yl The symbol 2 called sigma means add them all up X and y are both quantitative r positive association r negative association ralways falls between 1 and 1 Near 0 indicate weak straightline relationship r 1 or 1 only occur when the points lie exactly on the straight line 0 Correlation is not affected by a change in units of measurement 0 Correlation ignores distinction between variables changing which is labeled xand ydoes not affect it 0 Correlation is strongly affected by outliers o Is only for straightline relationships 0 Has no units of its own just a number Category of strength based on absolute value of correlation 0002 Very weak to negligible correlation 0204 Weak low correlation 0407 Moderate correlation 0709 Strong high correlation 0910 Very strong correlation Chapter 15 Describing Relationships Regression Prediction and Causation Regression line a straight line that describes how a response variable y changes with the explanatory variable X Often used to predict the value of y for given value of X Leastsquares regression line the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible Regression equation y a bx yintercept slopex To nd 1 Create a scatterplot and describe the form direction and strength of the relationship Look for outliers Remember you must have a fairly linear form to use correlation and regression 2 Compute the correlation coefficient r 3 Obtain the equation of the regression line y a bx yintercept slopex Note about slope the bigger the absolute value of it the steeper the line And slope and correlation always have the same sign Prediction Plug new values of x into the regression line to predict new y values Prediction outside the range of data extrapolation and leads to false predictions it s bad Regression in terms of correlation Correlation measures direction amp strength of a straightline relationship Regression draws line to describe this relationship 0 Both are strongly affected by outliers Usefulness of regression line for prediction depends on strength of association aka correlation between the variables 0 The square of correlation Rquot2 percent of variation in the y variable that is explained by the regression line Find the correlation square it then multiply it by 100 Is always between 0 and 100 closer to 100 stronger the linear relationship between x and y Causation Strong relationships between variables does not necessitate a cause effect relationship 0 Relationships between variables are often in uenced by lurking variables 0 Best evidence of causation comes from randomized comparative experiments 0 Even when direct causation is present it is rarely the complete explanation for the variables relationship 0 Three types of causation note two or more of these may happen simultaneously 0 Direct causation 0 Common response O Confounding Observed relationships can be used to make predictions without worry of causation as long as the patterns continue to hold true in data 0 Establishing causation without an experiment Criteria 0 O O 0 Association between variables is strong Association is consistent throughout many studies reduces effects of lurking variables Higher doses l stronger responses Alleged cause comes before effect chronologically Alleged cause is plausible Chapter 17 Thinking about Chance Chance random behavior in the short run unpredictable In the long run regular and predictable pattern 0 Random if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions Probability any outcome of a random phenomenon is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetitions 0 Probability 05 means occurs half the time in a very large number of trails Outcome with probability 0 never occurs 0 Outcome with probability 1 happens on every repetition quotLaw of averagesquot aka Law of large numbers Averages or proportions are likely to be more stable when there are more trials while sums or counts are likely to be more variable This does not happen by compensation for a bad run of luck since independent trials have no memory Note stable the average or proportion is likely to be closer and closer to the true population value Unstable the sumcount tends to vary father and father from the true value Personal Probability a number between 0 and 1 that expresses and individual s judgment of how likely the outcome is Advantage aren t limited to repeatable settings Useful because we base decisions on them They are opinions thus cannot be said to be right or wrong Note Probability in terms of quotpersonal judgment of how likely and probability in terms of quotwhat happens in many repetitions are two completely different ideas They are not two explanations of the same thing Chapter 18 Probability Models Probability model in terms of a random phenomenon describes all the possible outcomes and says how to assign probabilities to any collection of outcomes We sometimes call the collection of outcomes an event Rules that all probability models must obey 1 Any probability is a number between 0 and 1 because any proportion is a number between 0 and 1 2 All possible outcomes together must equal probability 1 3 The probability that an event does not occur 1 the probability that the event does occur 4 If two events have no outcomes in common the probability that one or the other occurs is the sum of their individual probabilities A probability is incoherent when it does not follow rules 1 amp 2 They don t go together in a way that makes sense Sampling distribution shows us how sample statistics can vary It is a probability model in that it assigns probabilities to the values the sample statistic can take In other words it is a collection of the values the sample statistic can take and how often it takes those values if we repeatedly sample from the same population Because there are usually many possible values sampling distributions are often described by a density curve such as a Normal curve In other words we can apply the rules of Normal distributions to answer questions about sample statistics Describing sampling distributions by shape center and spread variability o In certain conditions the sampling distribution will have normal shape 00gt an apply rules of normal distributions see above 0 Sampling distribution is centered where the population is centered Sampling distribution is less spread out or less variable than the population

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