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STAT 110 - Section 5 Lecture 6

STAT 110 - Section 5 Lecture 6. Professor Hao Wang University of South Carolina Spring 2012. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A. Last time . Population and Sample. (II) Sample variability. Example.

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STAT 110 - Section 5 Lecture 6

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  1. STAT 110 - Section 5 Lecture 6 Professor Hao Wang University of South Carolina Spring 2012 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

  2. Last time Population and Sample

  3. (II) Sample variability

  4. Example How many hours of sleep does an average USC undergrad have ? Ask your 2 neighbors and average their answers. A less than 5 hrs B 5-6 C 7-8 D 9-10 E more than 10 hrs Population ? Parameter ? Sample ? Statistic ?

  5. Example How many hours of sleep does an average USC undergrad have ? Ask your 5 neighbors and average their answers. A less than 5 hrs B 5-6 C 7-8 D 9-10 E more than 10 hrs Population ? Parameter ? Sample ? Statistic ?

  6. Sampling Variability bias – consistent, repeated deviation of the sample statistic from the population parameter in the same direction when we take many samples  systematically misses in the same direction variability – describes how spread out the values of the sample statistic are when we take many samples.  amount of scattering

  7. Picturing Bias and Variability

  8. Variability of 1,000 of size n = 100

  9. Variability of 1,000 of size n = 1,523 Notice that with larger samples (1523 vs. 100), there is a lot less variability….but the distribution is still centered at p = 0.60 (so p-hat is unbiased for p)

  10. http://www.rasmussenreports.com/public_content/politics/elections/election_2012/election_2012_presidential_election/florida/2012_florida_republican_primaryhttp://www.rasmussenreports.com/public_content/politics/elections/election_2012/election_2012_presidential_election/florida/2012_florida_republican_primary Example: 2012 Florida Republican Primary 10

  11. In the previous poll:A – The population is the 750 votersB – The population is all likely Florida voters

  12. In the previous poll:A – The percent of all likely FL voters favoring Gingrich is the Parameter and the 41% of the 750 is the statisticB – The percent of all likely FL voters favoring Gingrich is the statistic and the 41% of the 750 is the parameter

  13. In the previous poll:A – The variability is because Gingrich has been in the news a lot recently, and the bias is because it was a random sample.B – The variability is because it was a random sample, and the bias is because Gingrich has been in the news a lot recently.

  14. (III) Margin of Error

  15. Margin of Error • During the week of 8/10/01, CNN conducted a poll asking an SRS of 1000 Americans whether they approve of President Bush's performance as President. The approval rating was 57% (plus or minus 3%). In their next poll conducted during the week of 9/21/01, CNN conducted the same poll asking an SRS of 1000 Americans whether they approve of President Bush's performance as President. The approval rating was 90% (plus or minus 3%). • Why the difference in ratings? • Where does plus or minus 3% come from?

  16. Margin of Error The margin of error (MOE) is a value that quantifies the uncertainty in our estimate. When using the sample proportion to estimate the population proportion, the MOE is a measure of how close we believe the sample proportion is to the population proportion.

  17. Calculating Margin of Error • Use the sample proportion from a SRS of size n to estimate an unknown population proportion p. • For 95% confidence (the quick formula):

  18. Example: Margin of Error • The CNN Poll interviewed 1000 people. What is the margin of error for 95% confidence (using the quick formula)? Answer: Recall 95% confidence

  19. Example: Margin of Error If the sample size is 100, what is the margin of error for 95% confidence (using the quick formula)? 0.10% 0.01% 10%

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