STATSExam#2StudyGuide.pdf Stats 1350
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Date Created: 03/26/15
Midterm Exam 2 Study Guide week 7 10 Chapter 13 Normal Distributions Normal distribution perfectly symmetric about the mean one standard deviation is about one halfway up does NOT ever touch zero u mu this is the symbol for MEAN of the distribution the mean is the center of the distribution 0 sigma refer to this is the symbol for the STANDARD DEVIATION tells disperse or deviate value Empirical Rule 6895 997 draw picture of graph on cheat sheet bell shaped curve the total area under the curve is 100 gives a sense for where the data is at never touches zero 68 68 of the observation fall within 1 standard deviation sigma of the mean 2 between 1 and 1 95 95 of the observation fall within 2 standard deviations Zsigma of the mean 2 between 2 and 2 997 997 of the observation fall within 3 standard deviations 35igma of the mean 2 between 3 and 3 Standard score zscore the number of standard deviations that x is away from the mean Formula 2 data mean standard deviation Interpret zscore zscore number number of standard deviations from the mean relative to the group Negative zscore percentile lt 50 Positive zscore gt50 Zscore of 0 50 percentile Use zscores to find percentages Look at Table B and find the corresponding percentage Above certain score subtract from 1001 Below certain score keep what is read from the table B Forward problems quotwhat is the know observed value use table B to look at zscore and find percentile convert to 2 at the start Formula zscore observed mean standard deviation Backwards problems quotwhat is the observed value know the use table B to look at percentile and find zscore Formula observed mean standard deviation x zscore Find the percentage between two values find the zscore of both numbers and subtract the percentages from the table b Chapter 14 Describing Relationships Scatterplots and Correlation Scatterplot displays the relationship between two quantitative variables how the variables relate to each other use one variable to help explainpredict the other variable Form Shape Linear vs Nonlinear vs No obvious pattern Direction Slope and how steep Positive up left to right uphill as x increases so does y vs Negative down left to right downhill as x decreases so does y vs No association Strength correlation dots falling close to the line Strong very close vs Moderate pretty close vs Weak diffused from line Correlation coefficient r we need a linear relationship to use to tell something about the strength and direction of a relationship Correlation numerical description of the strength and direction of the linear relationship between x and y Decide if a relationship is strong moderate or weak 02 very weak correlation24 weaklow correlation 47 moderate correlation 79 stronghigh correlation9 1 very strong correlation Correlation coefficient between 1 to 1 1 perfect positive correlation 1 perfect negative correlation Correlation will be affected by outliers Correlation DOES NOT imply causation Correlation has no units Correlation between two variables will not change if the units of analysis change eg a change from pounds to kilograms or from dollars to cents etc Chapter 15 Describing Relationships Regression Prediction and Causation Response variable y we are attempting to predictexplain Explanatory variable x we are using to make the prediction Equation for a regression line y a bx A yintercept the y value when x is 0 where the line crosses the verticaly axis predicted value when x 0 B slope amount y changes when x increases by 1 the bigger the absolute value of the slope the steeper the line the slope and the correlation always have the same sign Regression equation and making a prediction use leastsquares regression line to find y for other x values with in the range of original data is great Extrapolation predicting using xvalues outside of the range of the original data bad it s not useful and can lead to false conclusions rsquared equals the percentage rquot2 take square root to find correlation What is necessary to conclude that one variable causes correlation is NOT causation sometimes it s just coincidence Only a well designed controlled experiment can show you causation still difficult to show Difference between Common response lurking variable Confounding occurs when the experimental controls do not allow the experimenter to reasonably eliminate plausible alternative explanations for an observed relationship between variables Chapter 17 Thinking about Chance Random chance behavior is unpredictable in the short run but has regular and predictable pattern in the long run Does NOT mean haphazard If individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large of repetitions random is the kind of order that emerges only in the long run Randomness is regular in the long run Probability a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetition Probability 0 it NEVER occurs impossible Probability 1 CERTAIN it will occur always Law of Averages Myth flipping a coin 9 times and get TTTTTTTTT the probability of the 10th coin toss being heads Probability is still 12 the coin doesn t look at the first 9 trials Successive deals are independent of each other More stable averagesproportions closer to the expected when there s a larger of trials More variable sumscounts farther from the expected when there s smaller of trials Shortrun regularity random phenomenon is not necessarily regular in the short run Personal probability guessing not based on datanot scientific Chapter 18 Probability Models Probability model random phenomenon describes all the possible outcomes and say how to assign probabilities to any collection of outcomes all outcomes and a probability for each Event collection of outcomes Probability Rules Number between 0 1 All possible outcomes together must have a probability 1 sum of all probabilities 1 The probability that an event does not occur is 1 minus the probability that the event does occur complement P not picking A 1 P A If two events have no outcomes in common the probability that one OR the other occurs is the SUM of their individual probabilities lfA and B have no outcomes in common P AorBPAPB Sampling distribution tells us what value the statistic takes in repeated samples as opposed to individuals from the sample population and how often it takes those values Described by shape center and spread variability Sampling distribution is centered where the population is centered expected sample result is population proportion The mean of the mean is the mean Sampling distribution is less spread out than the population standard deviation for x bar is smaller than standard deviation for x Determine probabilities based on knowing about the sampling distribution use 2 scores and table b
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