Chapter 9

Chapter 9 - Chapter 9 Hypothesis Testing Testing vs Estimation Confidence Intervals are used to estimate an unknown population parameter using

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 9 Hypothesis Testing
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Testing vs. Estimation ± Confidence Intervals are used to estimate an unknown population parameter using sample data. ± A Hypothesis test is used when theory suggests a particular value for an unknown population parameter. The question then becomes whether the sample data is consistent with the theory or not.
Background image of page 2
A Theory about the value of a population parameter? ± One popular test of ESP uses what is called a Rhine deck, which consists of cards with five different images on them. ± The cards are put in random order, and the subject must guess the card that has been drawn without seeing it.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The Rhine Deck and ESP ± The population parameter you are investigating is the proportion of correct answers in an infinitely long sequence of guesses. ± The sample statistic is the sample proportion of correct answers in a fixed number of guesses
Background image of page 4
The Theory ± There is one obvious theory here: Nothing is going on and the person is just guessing. By guessing the person should get 20% correct. This is the value of the population parameter we wish to test. ± Given sample data, such as 25 correct in 100 trials, the question becomes: Is this sample evidence enough to disprove the theory that the person is just guessing?
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The Null Hypothesis ± The theoretical value of the unknown population parameter we wish to test is called the null hypothesis . ± H 0 is the universal notation for a null hypothesis. ± Often the null corresponds to the idea “nothing interesting or unexpected is going on.” 00 0 : In this application, :. 2 0 Hpp Hp = =
Background image of page 6
The Alternative Hypothesis ± The alternative hypothesis comes in three flavors ² Less than ² Not equal to (two-sided) ² Greater than ± H-sub-A signifies the alternative hypothesis ± Which flavor is a matter of judgment: What do you expect to be true if the null is false? 0 0 0 : : : A A A H pp H H < >
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ESP and the Alternative Hypothesis ± If you believe that ESP (if it exists) will manifest itself in the person getting more than 20% correct, you’d do a greater than test. ± This leaves the possibility p < .20 hanging, so generally it is tossed into the null hypothesis. 0 0 :. 2 0 2 0 2 0 2 0 A A Hp = > >
Background image of page 8
Be careful about your notation! 0 0 2 0 Correct :1 2 :. 2 0 :7 H Hp H µ σ = = = ± Null and alternate hypotheses are always about unknown population parameters; they are never about sample statistics. 0 0 2 0 Incorrect 2 2 0 HX Hs = = =
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Isn’t this nitpicking? ± Confusing sample statistics and population parameters leads to complete nonsense. ± The statement is a perfect example. ² Before the sample is drawn, a sample statistic is a random variable, and therefore can’t be equal to a constant. ² After the sample is drawn, the sample mean is just a number. No fancy statistical theory is required to compare two known numbers. 0
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/01/2012 for the course ECON 371 taught by Professor Staff during the Spring '08 term at UVA.

Page1 / 144

Chapter 9 - Chapter 9 Hypothesis Testing Testing vs Estimation Confidence Intervals are used to estimate an unknown population parameter using

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online