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### 23 Cards in this Set

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 what is the standard deviation of population sampling distribution? square root [(p(1-p))/n] what is the distribution of the population proportion z statistic? approximately the standard Normal distribution N(0,1) if the sample is not too small and the sample is not a large part of the entire population conditions for inference about a proportion 1. Data is from an SRS 2. The population is at least 10 times as large as the sample. This condition ensures that the standard deviation of p has is close to the standard deviation 3. The saple size n is large enough to ensure that the distribution of z is close to standard normal. We will see that different inference procedures require different answers to the question "how large is large enough"? what is the plus four estimate? (count of successes in the sample +2 )/ (n+4) solving for the margin of error in population proportion problems 1. Use a guess p based on a pilot study or on past xperience with similar studies 2. Use p= 0.5 as a guess because the margin of error is largest when p hat is 0.5 so this guess is conservative in the sense that any other P will yield a smaller margin of error plus four interval for 2 proportions add one to the successes of each proportion and 2 to the n of each porportion regression line straight line that describes how a response variable y changes as an explanatory variable x changes. We often use a regression line to predict the value of y for a given value of x least square 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 equation for least square regression line y=a + bx slope r sy/sx intercept a = y bar -bx bar facts about least squares regressin lines 1. The slop equation says that a change of one standard deviation in x corresponds to a change of r standard deviations in y 2. The least square regression line always passes through the point (x bar, y bar) 3. r squared (variation in yhat as x pulls it along the line)/ (total variation in observed values of y) residual the difference between an observed value of the response variable and the value predicted by the regression line. Residual =observed y- predicted y influential observation if removing it would markedly change the result of the calculation. Points that are outliers in the x direction of a scatterplot are often influential for the least squares regression line extrapolation the use of the regression line for prediction far outside the range of values of the explanatory variable x that ou used to obtain the line lurking variable variable that has an important effect on the relationship among the variables in a study but is not included among the variables studied r squared = 0.207 tells you what? 21% of the variation in y is explained by x what are the paramters of a regression model? alpha (intercept), standard deviation of y, B (slope) the true regression line the mean response mu of y moves along a straight line as the explanatory variable x changes how do you test no correlation? Hnought: B= 0 SE sub mu hat confidence interval for predicting the mean response SE sub y hat a prediction interval for a single observation