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23 Cards in this Set
- Front
- Back
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what is the standard deviation of population sampling distribution?
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square root [(p(1-p))/n]
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what is the distribution of the population proportion z statistic?
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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
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conditions for inference about a proportion
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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"?
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what is the plus four estimate?
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(count of successes in the sample +2 )/ (n+4)
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solving for the margin of error in population proportion problems
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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
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plus four interval for 2 proportions
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add one to the successes of each proportion and 2 to the n of each porportion
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regression line
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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
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least square regression line
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the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible
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equation for least square regression line
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y=a + bx
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slope
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r sy/sx
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intercept
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a = y bar -bx bar
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facts about least squares regressin lines
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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.
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r squared
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(variation in yhat as x pulls it along the line)/ (total variation in observed values of y)
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residual
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the difference between an observed value of the response variable and the value predicted by the regression line. Residual =observed y- predicted y
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influential observation
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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
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extrapolation
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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
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lurking variable
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variable that has an important effect on the relationship among the variables in a study but is not included among the variables studied
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r squared = 0.207 tells you what?
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21% of the variation in y is explained by x
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what are the paramters of a regression model?
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alpha (intercept), standard deviation of y, B (slope)
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the true regression line
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the mean response mu of y moves along a straight line as the explanatory variable x changes
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how do you test no correlation?
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Hnought: B= 0
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SE sub mu hat
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confidence interval for predicting the mean response
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SE sub y hat
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a prediction interval for a single observation
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