1. When should you find the Confidence Interval, and when should you use a Hypothesis Test? Page 174

2. A May 2000 Gallup Poll found that 38% of a random sample of 1012 adults said that they believe in ghosts. Find a 95% confidence interval for the true proportion of adults who believe in ghost.

3. Find the confidence interval only. No hypothesis test is required.

4. Assumptions: Have an SRS of adults np =1012(.38) = 384.56 & n(1-p) = 1012(.62) = 627.44 Since both greater than 10, can approximate to normal. Population of adults is at least 10,120. Conclusion: We are 95% confident that the true proportion of adults who believe in ghosts is between 35% and 41%. AP Format Given: n = 1012 p =.38 q =.62 P hat =.38 x = (1012)(.38) = 385 Calculations:

5. A new flu vaccine claims to prevent a certain type of flu in 70% of the people who are vaccinated. In a test, vaccinated people were exposed to the flu. The test statistic for the results is z = -1.38. Is this claim too high?

6. Use a hypothesis test.

7. A new flu vaccine claims to prevent a certain type of flu in 70% of the people who are vaccinated. In a test, vaccinated people were exposed to the flu. The test statistic for the results is z = -1.38. Is this claim too high? Write the hypotheses, calculate the p-value & write the appropriate conclusion for  = 0.05. H 0 : p =.7 H a : p <.7 Where p is the true proportion of vaccinated people who get the flu P-value = normalcdf(-10^99,-1.38) =.0838 Since the p-value > , I fail to reject H 0. There is not sufficient evidence to suggest that the proportion of vaccinated people who do not get the flu is less than 70%.

8. Formula for hypothesis test:

9. P. 174 #2 A magazine is considering the launch of an online edition. The magazine plans to go ahead only if it’s convinced that more than 25% of current readers would subscribe. The magazine contacts a random sample of 500 current subscribers and 137 of those surveyed expressed an interest. Is this sufficient evidence for the magazine to start the online edition?

10. Use a hypothesis test.

11. Assumptions: Have an SRS of current subscribers np = 500(.25) = 125 & n(q) = 500(.75) = 375 Since both greater than 10, can approximate to normal. Population of subscribers is at least 5000. Conclusion: Since the p-value is greater than α, I fail to reject the null hypothesis. There is not sufficient evidence for the magazine to start the online edition. P. 174 #2 AP Format Given: n = 500, x = 137 p =.25 q =.75 p hat =137/500 =.274 Calculations: P-value = normalcdf(1.239,10^99) =.108 Hypotheses: H 0 : p =.25 α =.05 H a : p >.25 Where p is the true proportion of current readers who would subscribe.

12. REVIEW: Facts about p-values: ALWAYS make decision about the null hypothesis! Large p-values show support for the null hypothesis, but never that it is true! “Fail to reject” Small p-values show support that the null is not true. “Reject” Double the p-value for two-tail (=) tests Never acceptNever accept the null hypothesis!

13. At an  level of.05, would you reject or fail to reject H 0 for the given p-values? a).03 b).15 c).45 d).023 Reject Fail to reject Reject

14. Homework: Page 174: Determine which problems should use a Hypothesis Test, and rework those problems. Unit 10 Review #1-14 (Finish it) Quiz tomorrow