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Lecture

# confidence intervals and sampling

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University of Toronto St. George

Geography

GGR270H1

Damian Dupuy

Fall

Description

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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