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3. The Conservative Approach page 80 Margin of error = z* s.e.( ) = z* is largest when = ½ = 0.5. Conservative CI for a population proportion p What happens when z*=2 for 95% confidence?

4. Choosing a Sample Size (Conservative) Margin of error = Solve for sample size: Here you do ALWAYS round UP to next integer!

5. Try It! Coke versus Pepsi pg 81 a.What is the margin of error for this interval?. Poll in Canada to estimate p, the proportion of all Canadian college students who prefer Coke over Pepsi. A 95% conservative confidence interval for p was found to be (0.62, 0.70).

6. Try It! Coke versus Pepsi b.What sample size would be necessary for a conservative 95% confidence interval for p with a margin of error of 0.03 (width of 0.06)? Think about (c) and click in answer

7. c. Poll repeated in U.S. (popul 10 times larger than Canada), but four times the number of people interviewed. Resulting 95% conservative CI will be: A) twice as wide B) 1/2 as wide C) 1/4 as wide D) 1/10 as wide E) same width

8. RECAP: CI for a Population Proportion p page 79 Conservative CI for a Population Proportion p page 80 Conditions: 1.Sample is randomly selected sample from the popul. (Remember Fundamental Rule for Using Data for Inference). 2.Sample size n is large enough so the normal curve approx holds; i.e. np ≥ 10 and n(1–p) ≥ 10.

9. 10.5 Using CI to Guide Decisions pg 81 Principle 1 A value not in a confidence interval can be rejected as a possible value of the population proportion. A value in a confidence interval is an “acceptable” possibility for the value of a population proportion. Principle 3 When confidence intervals for proportions in two different populations do not overlap, it is reasonable to conclude that the two population proportions are different.

10. Coke versus Pepsi Do you think it is reasonable to conclude that a majority of Canadian college students prefer Coke over Pepsi? Think about it and click in your answer on next slide … Poll in Canada to estimate p, the proportion of all Canadian college students who prefer Coke over Pepsi. A 95% conservative confidence interval for p was found to be (0.636, 0.682).

11. A) Yes, because our 95% confidence level is larger than 50% (for a majority). B) Yes, because the entire interval of reasonable values for p is above 0.50 (for a majority). C) No, because this is just one interval, we need to look at all possible intervals. D) No, because we do not know p. Coke versus Pepsi … click in your answer Do you think it is reasonable to conclude that a majority of Canadian college students prefer Coke over Pepsi? Poll in Canada to estimate p, the proportion of all Canadian college students who prefer Coke over Pepsi. A 95% conservative confidence interval for p was found to be (0.636, 0.682).

12. Chpt 12 (Sections 1, 2, 3, 5) Testing about a p page 83 Basic Steps: 1:Determine null and alternative hypotheses. 2:Verify necessary data conditions, if met, summarize data into appropriate test statistic. 3:Assuming null hypothesis is true, find the p-value. 4:Decide if result is statistically significant based on p-value. 5:Report conclusion in context of the situation.

13. 12.2 Overview of Testing Hypotheses: Null hypothesis H 0 statement that nothing is happening status quo, no difference, no effect Alternative hypothesis H a statement that something is happening there is a difference, an effect researcher’s theory Statements about population not sample Direction of Extreme goes in Ha

14. Try It! Setting up Hypotheses 1. About 10% of human population is left-handed. Researcher speculates artists are more likely to be left-handed than in general population. H 0 :let___ = H a : Direction:

15. Try It! Setting up Hypotheses 2. Suppose that a pharmaceutical company wants to be able to claim that for its newest medication the proportion of patients who experience side effects is less than 20%. H 0 :let ___ = H a : Direction:

16. Try It! Setting up Hypotheses 3. US Census reports 48% of households have no children. Random sample of 500 households will be taken to assess if the population proportion has changed from the Census value of 0.48. H 0 :let ___ = H a : Direction:

17. Logic of Hypothesis Testing: What if null true? In a jury trail … H 0 : the defendant is _______________________ H a : the defendant is _______________________ Big Question: If null hypothesis is true about population, what is probability of observing sample data like that observed (or more extreme)?

18. Reaching Conclusions page 85 Deciding between two hypotheses using data. Data to be random sample from popul under study. Data summarized via a ______________________  Often standardized to measure distance between sample statistic and null value in standard error units.  Test Statistic = Sample Statistic – Null Value (Null) Standard Error

19. The p-value … p-value computed by assuming null hypothesis is true and determining probability of a result as extreme (or more extreme) as observed test statistic in the direction of the alternative hypothesis. Notes: (1) p-value is between 0 and 1, and is a conditional probability – probability of seeing a test statistic as extreme or more extreme than observed given null hypothesis is true. (2) p-value is not probability that null hypothesis is true. The __________________ the p-value, the stronger the evidence is AGAINST H 0.

20. Common Convention: Reject H 0 if the p-value is __________________ Borderline value called the _____________________ and denoted by _____. When the p-value ≤ , we say the result is _________________________________________ Common levels of significance: _______________

21. Two Possible Results: page 85 When p-value ≤ , we Reject H 0 and say the results are statistically significant at level  When p-value > , we Fail to Reject H 0 and say the results are not statistically significant at level  Always … write a real-world conclusion in sentence form in context of problem.

22. 12.3 Testing about a Population Proportion p page 86 1.H 0 : H a : 2.H 0 : H a : 3.H 0 : H a : Where does p 0 come from?

23. The Test Statistic Data provides estimate of population proportion p, namely sample proportion. For large sample size, the distribution of will be … We assume null hypothesis is true, p = p 0. So… If null hypothesis true, z-test statistic will have approximately a ____________ distribution.

24. Try It! Left-Handed Artists page 87 About 10% of human population is left-handed. Researcher speculates artists more likely to be left-handed. Sample of 150 artists  18 are left-handed. Perform test at 5% significance level. Step 1: Determine hypotheses H 0 :H a : where the parameter ________ represents … Direction:

25. Try It! Left-Handed Artists Step 2: Verify conditions, summarize via test stat. Data assumed to be a random sample Check np 0  10 and n(1 – p 0 )  10 Test statistic:

26. Try It! Left-Handed Artists Step 3: Find p-value. p-value = probability of getting a test statistic as extreme or more extreme than observed test statistic value, assuming the H 0 is true. We have one-sided test to right, toward larger values. p-value = probability of getting a z test statistic as large or larger than observed, assuming H 0 is true

27. Try It! Left-Handed Artists Step 4: Decide if result is statistically significant. Step 5: Report conclusion in context of situation.