1. Statistic for the day: The average distance that food travels to get to your table: 1300 miles Assignment: Read Chapter 3 Or Review for Midterm #3 These slides were created by Tom Hettmansperger and in some cases modified by David Hunter

2. perfect pitch These slides were created by Tom Hettmansperger and in some cases modified by David Hunter

3. perfect pitch (closeup)

4. A study to see if perfect pitch (the ability to reproduce music notes without reference to a standard) is related to a physical structure in the brain. Structure is called the planum temporale ( PT ) Using brain scans the PT surface area in mm 2 was measured for three groups: musicians with perfect pitch musicians without perfect pitch non-musicians without perfect pitch A measure of asymmetry in the PT was computed for each subject:

5. The researchers found: musicians with perfect pitch: mean dPT = -.57 musicians without perfect pitch: mean dPT = -.23 Question: Are the dPT means close or not? Is there a difference between musicians with and without perfect pitch? Equivalently we ask: Is the difference in means: -.57 – (-.23) = -.34 close to 0? What additional information do we need to answer the questions?

6. Answer: We must know either The sample standard deviation and sample size for each sample. Then compute the SEM for each sample. Remember: SEM = SD/sqrt(sample size) OR Be given the SEM directly and not have to compute it. In either case we can then use the Pythagorean theorem to find the standard deviation of the difference in means. sqrt[( SEM 1) 2 + (SEM 2) 2 ]

7. Sample Mean 1 Sample Mean 2 sample size 1 sample size 2 sample standard deviation 1: SD 1 sample standard deviation 2: SD 2 SEM 1: (SD 1)/sqrt(sample size 1) SEM 2 (SD 2)/sqrt(sample size 2) Standard deviation of the difference of sample Standard deviation of the difference of sample mean 1and sample mean 2: mean 1and sample mean 2: sqrt [ (SEM 1) 2 + (SEM 2) 2 ] To find standard deviation of difference

8. musicians perf pitch musicians no perf pitch means-.57-.23 samplesize1119 SD.21.17 SEM.019.039 Pythagoras SD of difference sqrt(.019 2 +.039 2 ) =.043 Diff in means = -.57 – (-.23) = -.34 So: -.34 + 2x(.043) or -.34 +.086 or -.43 to -.26 Conclusion: They are not close. There is a difference.

10. musicians perf pitch non-musicians means-.57-.23 samplesize1130 SD.21.24 SEM.019.044 Pythagoras SD of difference sqrt(.019 2 +.044 2 ) =.048 Diff in means = -.57 – (-.23) = -.34 So: -.34 + 2x(.048) or -.34 +.096 or -.44 to -.24 Conclusion: They are not close. There is a difference.

11. musicians no perf pitch non- musicians means-.23-.23 samplesize1930 SD.17.24 SEM.039.044 Pythagoras SD of difference Diff in means = -.23 – (-.23) = 0 Conclusion: They are close. There is no difference

12. General conclusions: There is a significant difference between the asymmetry of the PT for musicians with perfect pitch and both musicians without perfect pitch and non-musicians. This strongly suggests that there is a relationship between the physical structure of the PT in the brain and perfect pitch ability.

13. Questions: 1. Do PSU women carry more change than men? 2. Is there a greater proportion of women who carry change than for men? How to formulate question 1 in statistical terms: Is the mean amount of change carried by PSU women greater than the mean amount of change carried by men? Take samples of change from women and men and compare the sample means.

14. Sample Mean 1 Sample Mean 2 sample size 1 sample size 2 sample standard deviation 1: SD 1 sample standard deviation 2: SD 2 SEM 1: (SD 1)/sqrt(sample size 1) SEM 2 (SD 2)/sqrt(sample size 2) Standard deviation of the difference of sample Standard deviation of the difference of sample mean 1and sample mean 2: mean 1and sample mean 2: sqrt [ (SEM 1) 2 + (SEM 2) 2 ] To find standard deviation of difference

15. Stat 100: Men vs. Women Variable Sex N Mean StDev SE Mean -------- ------ --- ------ ------ ------- Age Female 133 19.624 3.320 0.288 Male 101 19.584 1.669 0.166 GPA Female 133 3.2186 0.4912 0.0426 Male 98 2.9863 0.5322 0.0538 Credits Female 136 15.566 2.073 0.178 Male 100 15.250 1.833 0.183 Studyhrs Female 136 2.941 1.761 0.151 Male 101 2.149 3.638 0.362 Phonmins Female 127 150.0 177.9 15.8 Male 96 91.1 111.2 11.4 Jeans Female 136 9.529 6.092 0.522 Male 98 5.684 3.283 0.332 CDs Female 135 85.4 116.3 10.0 Male 101 93.7 122.7 12.2 Cigpacks Female 136 0.419 1.227 0.105 Male 101 1.108 2.300 0.229