Testing Hypotheses About Proportions Ch. 20 Part 1 One-Proportion z-tests

Has the president’s approval rating changed since last month? Has teenage smoking decreased in the past 5 years? Is the global temperature increasing? Did the Super Bowl ad we bought actually increase sales? Examples of questions we might answer with hypothesis testing:

We first assume that there is no change. Our starting hypothesis is called the null hypothesis.

The complement of the null hypothesis is called the alternative hypothesis.

We are dealing with proportions, so the standard deviation and z-score are still the same for a one- proportion z-test:

4 Steps for a Hypothesis Test: 1)State the hypotheses. 2)Check conditions and model. 3)Mechanics (find z-score and p-value) 4)Conclusion

Stating hypotheses (Step 1): A large city’s Department of Motor Vehicles claimed that 80% of candidates pass driving tests, but a newspaper reporter’s survey of 90 randomly selected local teens who had taken the test found only 66 who passed. Does this finding suggest that the passing rate for teenagers is lower than the DMV reported? Write the appropriate hypothesis. The equal to part is always in the null hypothesis

Checking the Conditions and Modeling (Step 2): A large city’s Department of Motor Vehicles claimed that 80% of candidates pass driving tests, but a newspaper reporter’s survey of 90 randomly selected local teens who had taken the test found only 66 who passed. Does this finding suggest that the passing rate for teenagers is lower than the DMV reported? The 90 teens surveyed were a random sample 90 is fewer than 10% of teenagers who take driving tests in a large city np=90(0.8)=72; nq=90(0.2)=18

Mechanics: Find P-value (Step 3): A large city’s Department of Motor Vehicles claimed that 80% of candidates pass driving tests, but a newspaper reporter’s survey of 90 randomly selected local teens who had taken the test found only 66 who passed. Does this finding suggest that the passing rate for teenagers is lower than the DMV reported?

Stating conclusion (Step 4): A large city’s Department of Motor Vehicles claimed that 80% of candidates pass driving tests, but a newspaper reporter’s survey of 90 randomly selected local teens who had taken the test found only 66 who passed. Does this finding suggest that the passing rate for teenagers is lower than the DMV reported? Conclusion: With a p-value of , we fail to reject the null hypothesis. We can’t conclude that the passing rate for teenagers is lower than the DMV reported. (Next time we will discuss how to make the decision of rejecting the null or not.)

Practice writing the null and alternative hypotheses: A governor is concerned about his disapproval rate. His political committee pays for a series of TV ads, hoping they can keep the “negatives” below 30%. They will use follow-up polling to assess the ads’ effectiveness.

Practice writing the null and alternative hypotheses: Is a coin toss fair?

Practice writing the null and alternative hypotheses: Only about 20% of people who try to quit smoking succeed. Sellers of a motivational tape claim that listening to the recorded messages can help people quit.

Today’s Assignment:  Read Chapter 20!  No, really… read Chapter 20.  HW: page 476 #1, 2