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Welcome to BUAD 310

Welcome to BUAD 310. Instructor: Kam Hamidieh Lecture 15, Wednesday March 12, 2014. Agenda & Announcement. Today: Finish up Chapter 16. Reading for Chapters 16: ALL of it! Homework 4 has been posted & due Wednesday March 26, 2014, by 5 PM. Please watch the YouTube videos I posted.

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Welcome to BUAD 310

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  1. Welcome to BUAD 310 Instructor: Kam Hamidieh Lecture 15, Wednesday March 12, 2014

  2. Agenda & Announcement • Today: Finish up Chapter 16. • Reading for Chapters 16: ALL of it! • Homework 4 has been posted & due Wednesday March 26, 2014, by 5 PM. Please watch the YouTube videos I posted. • Do a midterm evaluation of me. • Next week: Spring Break. Have fun! BUAD 310 - Kam Hamidieh

  3. From Last Time (1-α)100% confidence interval for population proportion p using sample proportionis BUAD 310 - Kam Hamidieh

  4. From Last Time • Hypothesis testing: helps us draw inference about a population parameter of interest. • The possible values of the parameter of interested are partitioned into: • The probability question on which hypothesis testing is based: If the null hypothesis is true about the population, what is the probability of observing sample data like the one being observed? BUAD 310 - Kam Hamidieh

  5. Z-Tests for Proportion • Suppose now we want to make inference about the population proportion p. • We can form our hypotheses: • The logical structure and steps of the hypothesis testing does not change; only the parameter of interest changes. BUAD 310 - Kam Hamidieh

  6. Z-Tests for Proportion • Suppose we have a random sample of size n from a population with an unknown population proportion p. To test the H0 versus Ha, we assume H0 to be true and we compute the z statistic: where is the sample proportion… BUAD 310 - Kam Hamidieh

  7. Z-Test for Proportion …In terms of a standard normal random variable Z, the P-value for the test of H0 against Use this test as long as np0 and n(1-p0) ≥ 10 BUAD 310 - Kam Hamidieh

  8. Example The career services director of a University has said that 70% of the school’s seniors enter the job market in a position directly related to their undergraduate field of study. Conduct a hypothesis test for this claim (at the 5% level) using the fact that in a sample of 200 of the graduates from last year’s class, 66% have entered jobs related to their field of study. BUAD 310 - Kam Hamidieh

  9. In Class Exercise 1 Go to: http://www.gallup.com/poll/1645/Guns.aspx Conduct a hypothesis test to see if a majority of Americans feel that the laws covering the sale of firearms should be made more strict?. Use α = 5%, and n = 1,000. (Make sure you check sample size conditions.) Majority means over 50%. Use your z-table to get an approximate p-value (use your laptop if you have it with you.). BUAD 310 - Kam Hamidieh

  10. Types of Error • A type I error is made when we reject the null hypothesis given the null hypothesis is actually true • A type II error is made when we fail to reject the null hypothesis given the null hypothesis is false. • The probability of making a type I error is the significance level ; this was our cut-off. You actually set this value! BUAD 310 - Kam Hamidieh

  11. Trade-Off in Probability for Two Errors There is an inverse relationship between the probabilities of the two types of errors. Increase probability of a type I error => decrease in probability of a type II error BUAD 310 - Kam Hamidieh

  12. Decisions and Types of Error (From Learning from Data by Abu-Mostafa & Magdon-Ismail & Lin) • The final practical decisions must be made in the context of the problem at hand! • Consider this: Suppose a finger print system works as follows:H0: You’re not an intruder. vs. Ha: You are an intruder! • We have: • Type I Error = You are not an intruder but the system falsely claims you are an intruder • Type II Error = You are an intruder but we fail to detect you. • Consider two potential users: • Supermarket: uses it to see if you belong to a discount program. • CIA: uses it to let you access sensitive documents. • Which error is more important for the supermarket and the CIA? BUAD 310 - Kam Hamidieh

  13. Statistical Power • When the alternative hypothesis is true, the probability of making the correct decision is called the power of a test: Power = 1 – P(Type II Error) • The higher this value, the better! • The calculation of power can be quite complicated. BUAD 310 - Kam Hamidieh

  14. Meaning of “Significance” • Note:Statistical Significance ≠ Practical Significance • Statistical significance means that null hypothesis is inconsistent with the data. • The difference may not have practical implications. BUAD 310 - Kam Hamidieh

  15. For Fun! (Time Permitting) What do you think? http://www.businessinsider.com/odds-of-perfect-ncaa-buffett-bracket-2014-1 (Thank you Armando for forwarding this to me.) BUAD 310 - Kam Hamidieh

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