Hypothesis testing

1. Hypothesis testing • A hypothesis is a claim about the property of a population • Statistical studies propose, then reject or fail to reject hypothesis • Claim can be against a specific value (benchmark) • South students have an average IQ greater than 115 • Or the claim can be between two populations • South students have an average IQ greater than RBR students

2. Rare Event Rule • If, under a given assumption, the probability of a particular observed event is exceptionally small, we conclude that the assumption is probably not correct. • For example, if we assume a new drug is ineffectual, but 22 or ot 25 people experience improvement, is our assumptuion correct? • On the other hand, if 15 out of 25 people experinece improvement, is our assum,ption correct? • When you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth, - S. Holmes

3. Writing a Hypothesis • Hypothesis are specific • Last weekend’s musical was well-attended • Hypothesis are based on a measurable statistic • The average number of people attending the musical was high • Hypothesis are comparable • The average number of people attending the musical was more that 200 people per night • The average number of people attending this year’s musical was more than last year Last weekend’s musical was successful

4. Live Example • Hypothesis are specific • Hypothesis are based on a measurable statistic • Hypothesis are comparable Diamonds are a girl’s best friend

5. Your Turn • Hypothesis are specific • Hypothesis are based on a measurable statistic • Hypothesis are comparable Boys like cars

6. Null and Alternative Hypothesis • The next step in studying a claim is to form null and alternative hypothesis • Null hypothesis • Called H0 • Might be the claim to be studied • The result of the study will reject or not reject the null hypothesis • Alternative hypothesis • Called H1 • The claim that will be accepted if H0 is rejected • Usually, but not necessarily the opposite of the null

7. Identifying null and alternative • Put the specific claim or hypothesis to be tested into symbolic (mathematical) form • Write, in symbolic form, what must be true if the original claim is false • H0 will be the expression that contains the condition of equality, H1 will be the other • Which means that sometimes we will prove our claim by specifically disproving the opposite claim

8. For example • The average number of people attending the musical was more than 200 people per night • Let μ represent the average attendance • Here the null hypothesis is the original claim

9. Another example • South students have a mean IQ greater than 110. • Let μ represent the mean IQ of a south student • H1: μ > 110 • H0: μ  110 • Here the null hypothesis is the opposite of original claim. • We will be testing the original claim by reject or not rejecting the opposite

10. Live example/Your Turn • Claim: South students like ice cream • Claim: Watson is intelligent

11. Homework • Write the null and alternate hypothesis for the following claims • The mean time to build a house is 5 months • The mean volume of sales is more than $250,000 • The average number of students taking AP classes is at least 120 students • The average distance traveled by a commuter is 45.6 miles.

12. Homework • Write Null and Alternate hypothesis for the following claims. • American cars are reliable • Teenage drivers are unsafe • Taxes in New Jersey are too high • The Mets are a good baseball team