Jordan Baker Paul Wang Dennis Ling

1. Dennis vs. Paul Jordan Baker Paul Wang Dennis Ling

2. Question • If you know the answer to the question, please do not blurt it out or tell anyone • Given that one of us (Dennis Ling, Paul Wang) has scored a 2350 on the SAT, who do you think it is? • Please answer question 1 on your sheet (we will come back to it later)

3. Methodology • Interviewed thirty students face-to-face during first lunch (alternate asking the question) • After selecting someone, we flipped a coin • Heads—interview that person • Tails—move on to next person • Lurking variables • Previous background information on Dennis or Paul • Responses of nearby peers • Who asks the question/talks

4. Data 2350 Dennis vs. Paul Graph Number of Votes 21 9

5. Parameter and Hypotheses • Parameter • p = true proportion of Bellevue High School students who have first lunch who think that Dennis Ling earned the 2350 • Hypotheses • H0: p = 0.50 • Ha: p ≠ 0.50

6. Conditions • Randomness—sample of 30 BHS students was taken randomly • Independence • N≥10n • N≥300 Thus, 10% condition is met. • Normality • np≥10 15≥10 • n(1-p)≥10 15≥10 Safe to assume sampling distribution is approximately normal.

7. Calculations: 1-proportion z-test • α-level = 0.05 • p̂ = 0.3 • po= 0.5 • n = 30 • z = -2.191 • p(-2.191 ≥ Z ≥ 2.191) = .0285

8. Calculations: 1-proportion z-interval • 90% Confidence interval • p̂±z*√(p̂(1-p̂)/n) • p̂ = 0.3 • z* = 1.645 • n = 30 • Confidence Interval= (0.16238, 0.43762)

9. Interpretations • P-Value • We will reject the null hypothesis because our • p-value of 0.0285 is smaller than the α-level of 0.05. Therefore, we do have strong evidence that the proportion of people at BHS who feel that Dennis Ling scored a 2350 on the SAT is not equal to 0.50. • Confidence interval • We are 90% confident that the true proportion of Bellevue High School students who have first lunch who think that Dennis Ling earned the 2350 is between 0.162 and 0.438. This agrees with our above conclusion with the p-value because zero is not included in the confidence interval.

10. Potential Error • We thought that the weight of Type 1 and Type 2 errors were about the same, so we kept the α-level as 0.05 • We could have made a Type 1 error because we rejected the null hypothesis • If the null is actually true, then we made a Type 1 error

11. General Conclusions • More people think Paul Wang earned the 2350 on the SAT • A 2350 on the SAT is generally considered fairly accomplished, so we came to the conclusion that Paul Wang appears to be smarter-looking than Dennis Ling

12. Who do you think earned the 2350? • What did you write down for question 1? • The correct answer is…

13. D

14. E

15. N

16. N

17. I

18. S

19. JK…