Automotive Technology The following table shows the U.S. Environmental Protection Agency (EPA) fuel economy values for selected two-seater cars for the 2009 model year. (Source: http://www.fueleconomy.gov.) EPA Fuel Economy Values for Selected Two-Seater Cars Car City (mpg) Highway (mpg)Audi, TT Roadster 22 30BMW, M6 11 17Ferrari, 599, GTB 11 15Lamborghini, L-174 12 20Chevrolet, Corvette 14 20Maserati, Gran Turismo 12 19a. Using the data for the Lamborghini and the Audi, find a linear function that predicts highway miles per gallon in terms of city miles per gallon. b. Using your model, predict the highway miles per gallon for a Porsche Targa, whose city fuel efficiency is 18 miles per gallon

April 4th Frequency Distributions and Histograms show how frequent diﬀerent values are for a variable Mean, Median, and Mode from Frequency Table mean: (ΣX)/n median: (n+1)/2 mode: most frequently occuring Characteristics of Means changing the value of a score changes the mean introducing a new score or removing a score changes the mean unless the score added or removed is exactly equal to the mean adding or subtracting a constance from each score changes the mean by the same constant multiplying or dividing each score by a constant multiples or divides the mean by that constant. Graphing Frequencies: Histograms one of the most common ways to explore data graphically clusters adjacent scores together to show the gist of trends in the data tells us a lot about the shape of distribution Bar Graphs vs Histograms Histograms: continous variables has bars that touch bars represent frequencies of ranges of scores Bar Graph usually nominal discrete variables bars don’t touch Distributions: described by words skewed, nominal, bimodal, symmetrical described by pictures described by numbers mean, median, mode standard variation, variance Normal or Gaussian Curve relative frequency (no #s on y-axis) many naturally occurring distributions approximate this curve mean, median, and mode are the same Skewed Distribution tail goes out left → negative distributions (median higher than mean) tail goes out right → positive distributions (mean higher than median) Shade Implications for Central Tendency Negative skew: >50% will be above average Positive skew: >50% will be below average use median for seriously skewed data April 11 Variance and Inferential Statistics goal for inferential statistics is to detect meaningful and signiﬁcant patterns in research results variability in the data inﬂuences how easy it is to see patterns error variance: variability due to error Sums of Squares: SS = Σ(X-M)^2 Variance: population: Ơ^2 = SS/N sample: S^2 = SS/n-1 Standard Deviation population: Ơ = √SS/n sample: S = √SS/n-1 How to Interpret Standard Deviation Conceptually standard deviation is the typical distance of the scores to the mean same thing as variance, just take square root so it’s easier to interpret Z-Scores identify and describe location of every score in the distribution standardize an entire deviation takes diﬀerent distributions and makes them equivalent and comparable one we know the mean and standard deviation of scores, we can turn any raw score into a standardized score (z-score) allows us to know the exact location of x in the distribution of scores sign tells us if it’s above or below the mean # tells us distance between score and mean need to know the value of X, M, and SD to understand exact location all 3 pieces combine to make 1 value population z-score: (X-M)/Ơ, sample z-score: (x-m)/s Properties of Z-score Distributions mean is always 0 SD is always 1 when an entire set of scores is transformed into z-scores, it’s called a standard deviation Uses for Z-scores (examples) compare same person across diﬀerent measures compare diﬀerent people on same test compare diﬀerent people on across multiple measures April 13 Probability: # desired outcomes/#possible outcomes Probability ratio of a given outcome to all possible outcomes ranges from 0 to 1 probability is a proportion Probability is NOT the Same as Odds odds = #desired outcomes/#undesired outcomes Probability and Statistics random sampling is necessary in order for certain properties of probabilities to hold true requires that each individual in the population has an equal chance of being selected (nothing “loaded”) requires sampling with replacement probabilities of being selected must stay constant from one selection to the next Standardized Distribution z-scores are used to denote the precise location of a raw score Z = (X-M)/Ơ Standardized Normal Distribution due to mathematical properties of the normal distribution, when standardized, proportions of area under the curve correspond to speciﬁc z-scores Note: z-scores can be computed for any distribution you can only use a z-score to calculate probability if the distribution is normal Area Under the Curve the total area under the normal curve is 1 z-scores will divide the distribution into the tail and body z-scores above the mean are positive, below the mean are negative, but proportions will always be positive because z-scores deﬁne the sections, the proportions of the area apply to any normal distribution distribution is symmetrical so proportion of + and - z-scores are the same The Unit Normal Table (this is found in Appendix B in your book!) the proportion for only a few z-scores can be shown graphically How to use: If Z is positive probability of score >Z is the tail probability of score Z is body probability of score