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confidence intervals and sampling

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University of Toronto St. George
Damian Dupuy

Statistics Lecture November 2, 2011 Assignment: you don’t have to repeat covariance but you have to say where you got it from; such as I got it from part A Correlation: relationship between them Regression: one causes the other Y is a function of X; changes in Y are changes in X Precipitation is a function of temperature Changes in temperature are independent Precipitation on Y axis, temperature on the X axis Show the mean of x and draw a dotted line across and same for Y Confidence Intervals • Most often you don’t know how precise the single sample mean as an estimator ex. Smaller sample sizes • Place interval around the sample mean and calculate the probability of the true population mean falling within this interval • Giving a reference point to the sample mean and saying its in there and we are confident that it is in there • Can say, with a measureable level of confidence, that the interval contains the true population parameter • Ex. Placing confidence interval around our mean [sample mean] Say with 90% confidence the interval range contains the population mean Xbar +/- Z (sXbar) Xbar= sample mean Z= z value from the table sXbar= standard error of the mean We need to know the Z value 90% chance inside the interval, 10% outside it 100% confidence is the population and 99% is the most because it can never be absolute Each side of the curve is 50% of the diagram. So 5% confidence on each side on the outside and 45% inside the interval 1.65 [one of the four you’ll always have to use] Xbar +/- 1.65 standard error of the mean *you often see it as 1- a a= significance level 90% level of confidence, we have a 10% significance level • What does it mean if you are 95% confident? • If you constructed 20 intervals, each with a different sample information, 19 out of 20 would contain the population parameter (greek letter m) and 1 would not • But, we can never be sure whether a particular in
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