1. Course Extra for Part II

2. Quizzes  Any questions from the quizzes?

3. Study Guide  Any questions from the study guide?

4. Formulas Given What does a z-score actually mean? What is its unit of measurement?

5. Given

6. Understanding Confidence Intervals You take a random sample of 35 EMU students and record the time that it takes each of them to run a mile. A 95% confidence interval for the population mean is calculated to be (7:54, 8:43). Based on this interval, what could you say about the claim that the actual mean for all EMU students is 8:30? - We can’t make any statements about the claim without the p-value. - We have evidence that the mean for all students is 8:30, because it’s inside the interval. - We have convincing evidence that the mean is not 8:30, because it’s near the edge of the interval. - We don’t have evidence that the mean differs from 8:30, because 8:30 is inside the interval.

7. Do hints help on a cryptogram?  Students are randomly assigned into either the treatment (i.e., given hints) or no treatment (i.e., no hints) group and are then given a cryptogram to decipher. The time (in seconds) is recorded when the student solves the puzzle, with a maximum of 480 seconds.cryptogram  Does having the hints significantly lower the time required to solve the puzzle?

8. Cryptogram Results HintsNo Hints 480 457480 243480 428480 369480 470480 436480 460480 455480 413480 465390 x bar 439.7474 s 62.823.2 st error 16.26 95% Lower 408.0462.2 95% Upper 471.5485.8

9. Cryptogram Results

11. Statistical Results (we’ll interpret these in Chapter 18) t-Test: Two-Sample Assuming Unequal Variances Variable 1Variable 2 Mean439.7333333474 Variance3941.209524540 Observations15 Hypothesized Mean Difference0 df17 t Stat-1.98253044 P(T<=t) one-tail0.03191014124 t Critical one-tail1.739606668 P(T<=t) two-tail0.06382028248 t Critical two-tail2.109815559

12. Conclusions for Cryptogram Experiment  What would our decision be regarding the null?  What does this mean in common English?  What error could we have made?  What’s the chance that we made that error?

13. Additional Review  What does the Central Limit Theorem tell us?  Give an example of a research question that probably cannot be addressed with an experiment.  Random sampling vs. random assignment  What does the 95% mean in a 95% confidence interval?  How do you calculate a confidence interval?  How do you calculate a p-value?  Could you calculate a “confidence interval” around the population mean?