ECON2209 Lecture Notes - Lecture 12: Standard Error, Null Hypothesis, Confidence Interval
8 Jun 2018
School
Department
Course
Professor
February 27th
Problems
● Standard error of the mean…. Take sample standard deviation and divide by the square root
of n
● Consider the following data set: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31. Find
the second decile. Make sure to round your answers to the nearest 100th percentage point.
○ Answer: 5.8
○ How to do this problem
■ N = 16
■ Location = L20
■ L20 = (16+1) * (20/100) = 3.4
■ So somewhere between the 3rd and 4th observation
■ 1, 3, 5, 7 ….
■ Between 5 and 7
■ 5 + .4(7-5) - 5.8
● Estimation:
○ “Confidence interval”
■ (1-alpha)*100% confidence interval
■ Estimation for u (CI for u)
■ If n is very large, t approaches z
○ THURSDAY TOP HAT: N = [Zsigma/2*(sigma/B)]2
● Hypothesis testin
1. Write the null hypothesis
March 1st
● Interpretation of the confidence interval: (1-alpha)/CI
○ We are (1-alpha)100% confident that the true value falls in the interval constructed
○ We are 95% confident that the true ____ value, falls between the interval we just
constructed
○ The Confidence is not in the interval itself, BUT in the process
○ If we could construct all possible intervals, using all possible sample values, and
using this process, than (1-alpha)*100% of these intervals will contain the true value
○ The interval constructed, has a (1-alpha)% chance of containing true value and a
alpha(100%) chance of not containing the true value
● Regression
○ Linear
○ Assumptions
○ Estimated model → OLS
○ Estimated variance and standard deviation of error term (E)
○ Estimation of beta’s
○ Estimation of the coefficients
○ Inferences: Test of gammas
○ Testing the overall utility or usefulness of the model
find more resources at oneclass.com
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Document Summary
Take sample standard deviation and divide by the square root of n. Consider the following data set: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31. Make sure to round your answers to the nearest 100th percentage point. So somewhere between the 3rd and 4th observation. If n is very large, t approaches z. Hypothesis testin: write the null hypothesis. We are (1-alpha)100% confident that the true value falls in the interval constructed. We are 95% confident that the true ____ value, falls between the interval we just constructed. The confidence is not in the interval itself, but in the process. If we could construct all possible intervals, using all possible sample values, and using this process, than (1-alpha)*100% of these intervals will contain the true value. The interval constructed, has a (1-alpha)% chance of containing true value and a alpha(100%) chance of not containing the true value.
