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

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

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

Live Example

• Hypothesis are specific

• Hypothesis are based on a measurable statistic

• Hypothesis are comparable

Diamonds are a girl’s best friend

Your Turn

• Hypothesis are specific

• Hypothesis are based on a measurable statistic

• Hypothesis are comparable

Boys like cars

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

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

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

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

Live example/Your Turn

• Claim: South students like ice cream

• Claim: Watson is intelligent

Homework

• Write the null and alternate hypothesis for the following claims

1. The mean time to build a house is 5 months

2. The mean volume of sales is more than $250,000

3. The average number of students taking AP classes is at least 120 students

4. The average distance traveled by a commuter is 45.6 miles.

Homework

• Write Null and Alternate hypothesis for the following claims.

1. American cars are reliable

2. Teenage drivers are unsafe

3. Taxes in New Jersey are too high

4. The Mets are a good baseball team