1. m&m’s Track Record Since 1997 Fontainebleau Singapore

2. AVERAGE No. of M&Ms/bag IN EACH SECTION (for 5 promotions between Jan 01-Sep 03) Mean45,50 Std Dev0,4671

3.     Z  1.96 95% An Illustration of the derivation of 95% confidence intervals.

4. From the diagram, we can write: Algebra 95% Confidence Intervals

5. Standard Error of the Sample Mean if we know sigma (session 6) if we don’t know sigma, then This is legitimate because:

6. X -   / n  Z Case 1:  is known, n  30 Confidence Interval Limits X -  s/ n  Z Case 2:  is unknown, n  30 Estimating 

7. Interested in x/n x = # of people who: (a) Prefer Candidate A over the other candidates (b) Prefer Brand A over the other brands (c) Have tried or done _____ (fill in the blank) n = A sample from the relevant population Objective Estimate p, the true population proportion Results

8. p    Z .96 95% An Illustration of the derivation of 95% confidence intervals for proportions.

9. 95% Confidence Interval for Proportions

10. “Results are based on telephone interviews with 1,025 national adults, aged 18 and older, conducted Sept. 8-10, 2003. For results based on the total sample of national adults, one can say with 95% confidence that the maximum margin of sampling error is ±3 percentage points. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls.” --- Gallup web site State of the Nation George W. Bush Approval Rating

11. Swedish Euro Vote Sunday September 14, 2003

12. Moral Values Gallup Personal Interviews: 1000 adults per country February - May 1997 Do you think it is, or is not, morally wrong for a couple to have a baby if they are not married?

13. Margin of Error E as a Function of x/n  = 0.05 n = 1,000 x/n Margin of Error

14. Margin of Error E as a Function of n and x/n  = 0.05 x/n Margin of Error n = 250 n = 500 n = 1000

15. American Intelligence GallupTelephone Survey: 1016 adults June 25-27, 1999 As far as you know, does the Earth revolve around the Sun, or does the Sun revolve around the Earth? Earth around Sun:79% Sun around Earth:18% No opinion:3%