2. Back to the Z Joint

3. Decide if the following situations call for a mean or a proportions: The Center for Disease Control took a random sample of 165 patients with the flu virus and found that only 8% of them had received a flu shot. Based on this information is there significant evidence to conclude that a flu shot is effective at 5% significance? The CDC took a random sample of 250 flu shots administered in the month of February and found the average number of faulty vaccines was 4.5. Is this significant evidence to prove the national average of 5.2 faulty vaccines is actually lower? Proportion Mean

4. For Proportions, p is the population proportion p-hat is the Statistic (sample proportion. p-hat = # of successes in sample # of observations in sample Tierney wants to estimate the proportion of people that prefer Graeter’s brand ice cream to Kroger brand. She takes a random sample of 165 people in her hood and finds that 35 of them prefer Kroger’s ice cream. What is the p-hat for Tierney’s study?

5. To carry out inferences for proportions we are using the sampling distribution of p-hat. We have 3 Conditions for this Inference: Data are an SRS from the population Population is at least 10 times the sample size For Hypothesis Test: np o and n(1-p o ) are both greater than 10 For Confidence Interval: n(p-hat) and n(1-p-hat) are greater than 10

6. We are using the z(normal) distribution. The z statistic Standard Error Confidence Interval Based on Confidence Level Significance Testing We use all the same steps that we have been using, we are just using the z-statistic above and the z-chart…

7. A poll for the question, “Have efforts to promote equality for women gone far enough in the US?”, answered by 1029 adults found that 54% said “Yes.” Find a 95% Confidence Interval for the proportion in the adult population who would say “Yes” if asked. =.5095 -.5705

8. Sometimes we are asked to determine the sample size necessary to reach a certain margin of error The margin of error formula looks like… z* = z according to Confidence Level m = Margin of Error p* = guessed p-hat value based on previous study

9. Austin and Jeremy are running for Stat Class President. You are planning a sample survey to determine what percent of the voters plan to vote for Jeremy. You contact an SRS of the eligible voters and want to estimate p with 95% confidence and a margin of error greater than 3%. We will guess the p* to be 0.5. n = 1067.1

10. H a = p > p 0 H a = p < p 0 H a = p ≠ p 0

11. In a recent year, 73% of first-year college students responding to a national survey identified “being very well- of financially” as an important personal goal. A state university finds that 132 of an SRS of 200 of its first-year students say that goal is important. Is there good evidence that the proportion of all first-year students at this university who think being very well-off is important differs from the national value, 73% at the 5% alpha? H o : p =.73 H a : p ≠.73 1)SRS 2)200(.73) = 146; 3)200(.27) = 44 z = -2.23 p = 2(.0129) =.0258 We have statistically significant evidence to reject the H 0 at the 5% significance level because our p value is less than.05. We can say that the national average of 1 st year college students that have a personal goal of being well off financially is different from 73%.

12. Z-Test for Population Mean Testing for Mean and have σ T-Test for Population Mean Testing for Mean and have s T-Test for Difference Between Means Matched Pairs Situation, Difference Between Means 2 Sample T-Test for Population Mean Testing for Difference Between Means with s (Not Matched Pairs) Z-Test for Population Proportion Testing for Population Proportion

13. Chapter 12 #’s 13-15,17-19