Chapter 20 1-Proportion Z-Test

1. Chapter 201-ProportionZ-Test

2. Take a sample & find . But how do I know if this is one that I expect to happen or is it one that is unlikelyto happen? How can I tell if this is accurate? Example :School administrators make the claim that 85% of Mauldin High School students carry a cell phone. A hypothesis test will help me decide!

3. What are hypothesis tests? Is it one of the sample proportions that are likely to occur? Calculations that tell us if a value, like p-hat, occurs by random chance (as a result of sampling variability) or not – ie, if it is statistically significant Is it . . . • a random occurrence due to natural sampling variability? • a biased occurrence due to some other reason? Is it one that isn’t likely to occur? Statistically significant means that it is NOT a random chance occurrence!

4. Nature of hypothesis tests - How does a murder trial work? • First begin by supposing the “effect” is NOT present • Next, see if data provides evidence against the supposition Example: murder trial First, assume that the person is innocent. Then, you must have sufficient evidence to prove guilty Hmmmmm … Hypothesis tests use the same process!

5. PHANTOMS Steps: define the Parameter Hypothesis statements Assumptions/conditions Name the test Test statistic Obtain a p-value Make a decision State a conclusion in context

6. Writing Hypothesis statements: • Null hypothesis – is the statement being tested; this is a statement of “no effect” or “no difference” or “nothing unusual” (the “dull” hypothesis) • Alternative hypothesis – is the statement that we suspect is true H0: HA:

7. The form: Null hypothesis H0: parameter = hypothesized value Alternative hypothesis Ha: parameter > hypothesized value Ha: parameter < hypothesized value Ha: parameter = hypothesized value Remember that hypotheses: ALWAYS refer to populations (parameters)

8. EXAMPLES: • Write the null and alternative hypotheses you would use to test each situation. • A governor is concerned about his “negatives” – the percent of state residents who disapprove of his performance. His political committee pays for a series of TV ads, hoping they can keep the negatives below 30%. They use a poll to test the ads’ effectiveness. • Is a coin fair? • Only about 20% of people who try to quit smoking succeed. Sellers of a smoking cessation program that their method can help people quit. p = .3 H0: HA: p < .3 H0: HA: p = .5 p ≠.5 p = .2 H0: HA: p > .2

9. Assumptions for z-test: Have a SRS Sample is less than 10% population np and nq are both at least 10 YEA – These are the same assumptions as confidence intervals!! Use p from the null hypothesis

10. Name the test: 1-proportion z - test

11. Test statistic (a.k.a. “z”):

12. P-values - • Assuming H0 is true, it’sthe probability that the test statistic (z) would have a value as extreme or morethan what is actually observed

13. If p is low, reject the Ho Statistically significant – • If p-value is small, “reject” the null hypothesis (Ho). • If p-value is large, “fail to reject” the null hypothesis (Ho).

14. How small does the p-value need to be in order for you to reject the null hypothesis? Level of significance - • Denoted by a • Can be any value • Usual values: 0.1, 0.05, 0.01 • Most common is 0.05 Reject Ho when the p-value is as small or smaller than the level of significance (a)

15. Facts about p-values: • The p-value helps you make a decision about the null hypothesis • Large p-values show support for the null hypothesis, but never proves that it is true! • Small p-values show support that the null is NOT true. • Double the calculator value for the p-value of two-tail (≠)tests • Never accept the null hypothesis! (“fail to reject”)

16. Never“accept” the null hypothesis!

17. At an alevel of .05, would you reject or fail to reject H0 for the given p-values? • .03 • .15 • .45 • .023 Reject Fail to reject Fail to reject Reject

18. Draw & shade a curve & calculate the p-value: 1) right-tail test z = 1.6 2) left-tail test z = -2.4 3) two-tail test z = 1.8 P-value = .0548 P-value = .0082 P-value = (.0359)2 = .0718

19. When p-value is small Make a Decision: “Since the p-value (state p-value) is < a(state α) , I reject the H0.” Be sure to write Ha in context (words)! State a conclusion in context: “There is sufficient evidence to suggest that Ha.”

20. When p-value is large Make a Decision: “Since the p-value (state p-value) is > a(state α) , I fail to reject the H0.” State a conclusion in context: “There is not sufficient evidence to suggest that Ha.”