1. Stat 217 – Day 21 Cautions/Limitations with Inference Procedures

2. The plan HW 5 being returned HW 6 due, solutions posted this evening Review day tomorrow Exam on Thursday in Library  Review sheet posted

3. Last Time – Two sample z procedures If goal is to compare two population proportions  Random assignment (treatment probabilities): AZT vs. Placebo  Independent random samples: men vs. women  Ho:  1 –  2 = 0 (  1 =  2 )  Ha:  1 –  2, ≠ 0 (  1, ≠  2 )

4. Activity 21-2 (p. 419) Random samples from population  “Samples are independent from one another because they’re picking new parents each year”  Responses should not be influencing each other Ho:  92 –  96 = 0; Ha:  92 -  96 > 0  “We expect to show a decrease in infants from sleeping on their stomach in 1996 vs. 1992” in entire population

5. Activity 21-2 Based on these numbers we can reject the null hypothesis in favor of the alternative. The p-value which is approximately 0 gives strong evidence that the proportion of babies in the population slept less on their stomachs in 1996 than in 1992. We have 95% confidence the population proportion of the 1992 babies on their stomachs is between.421 and.499 higher than in 1996. We cannot assume causation since no treatments were imposed. But since there was random sampling we can generalize our results to the populations.

6. Rest of Topic 21 Activity 21-3: Same procedure with randomized experiments but can draw cause- and-effect conclusions (but may not be generalizing) Activity 21-4: Larger samples lead to smaller p-values (all else the same)  71% vs. 81% Activity 21-5: Don’t jump to cause and effect conclusions!

7. Handout See overview of statistical procedures handout  Which procedures Self-test Work on examples, practice with technology and more subtle issues with inference, solutions posted this evening

8. Handout 1. Let  represent the proportion of all American households with a pet cat 2. H 0 :  = 1/3 (one-third of all American households have a cat) H a :  ≠ 1/3 (the population proportion differs from one-third) 3. one sample proportion z-test Random sample? Told only that it was a national sample so not clear but may be able to assume random. Sample size? n ×  = 80,000(1/3) = 26666.67; n × (1-  ) = 80,000(2/3) = 53333.33. Both exceed 10.

9. Handout The super small p-value (very large test statistic in absolute value) tells us that we have very strong evidence that the population proportion differs from 1/3. The confidence interval tells us that the population proportion is not all that far from 1/3. Not very different. Statistical significance vs. practical significance