Case Closed
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Case Case Closed Closed The New SAT The New SAT Chapter 2 Chapter 2 AP Stats at LSHS AP Stats at LSHS Mr. Molesky Mr. Molesky
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Case Closed. The New SAT Chapter 2 AP Stats at LSHS Mr. Molesky. ≈N(516, 115). 700. %Below 700≈.9452. %Below 600≈.7673. 600. 516. SAT Writing Scores. %Between 600 and 700≈.9452-.7673≈.1779. I: Normal Distributions. 1. SAT Writing Scores are N(516, 115) - PowerPoint PPT Presentation
Transcript of Case Closed
Case Case ClosedClosedCase Case
ClosedClosedThe New SATThe New SAT
Chapter 2Chapter 2
AP Stats at LSHSAP Stats at LSHSMr. MoleskyMr. Molesky
The New SATThe New SATChapter 2Chapter 2
AP Stats at LSHSAP Stats at LSHSMr. MoleskyMr. Molesky
I: Normal Distributions•1. SAT Writing Scores are N(516, 115)
What percent are between 600 and 700?
z700 700 516115
184
1151.6
z600 600 516115
84
1150.73
516SAT Writing Scores
≈N(516, 115)
600700
%Between 600 and 700≈.9452-.7673≈.1779
%Between 600 and 700≈.9452-.7673≈.1779
%Below 700≈.9452%Below 700≈.9452
%Below 600≈.7673%Below 600≈.7673
I: Normal Distributions•1. SAT Writing Scores are N(516, 115)
What score would place a student in the 65th Percentile?
516SAT Writing Scores
≈N(516, 115)
?
0.65
?mean 0.39(s)
?516 0.39(115)?516 44.85?560.85
Table A Standard Normal probabilities (continued)
z 0.00 0.01 ... 0.07 0.08 0.09
0.0 0.500 0.5040 ... 0.5279 0.5319 0.5359
... ... ... ... ... ... ...
0.3 0.6179 0.6217 ... 0.6443 0.6480 0.6517
0.4 0.6554 0.6591 ... 0.6808 0.6844 0.6879
Table A Standard Normal probabilities (continued)
z 0.00 0.01 ... 0.07 0.08 0.09
0.0 0.500 0.5040 ... 0.5279 0.5319 0.5359
... ... ... ... ... ... ...
0.3 0.6179 0.6217 ... 0.6443 0.6480 0.6517
0.4 0.6554 0.6591 ... 0.6808 0.6844 0.6879
z0.65 0.39 Table A Standard Normal probabilities (continued)
z 0.00 0.01 ... 0.07 0.08 0.09
0.0 0.500 0.5040 ... 0.5279 0.5319 0.5359
... ... ... ... ... ... ...
0.3 0.6179 0.6217 ... 0.6443 0.6480 0.6517
0.4 0.6554 0.6591 ... 0.6808 0.6844 0.6879
II: Comparing Observations• 2. Male scores are N(491,110)
• Female scores are N(502,108)
• a) What % of males earned scores below 502?
491Male Writing Scores
≈N(491,110)
502
z 502 491110
z 0.1%below .5398
II: Comparing Observations• 2. Male scores are N(491,110)
• Female scores are N(502,108)
• b) What % of females earned scores above 491?
502Female Writing Scores
≈N(502,108)
491
z 491 502108
z 0.101%below .4602
%above 1 .4602.5398
II: Comparing Observations• 2. Male scores are N(491,110)
• Female scores are N(502,108)• c) What % of males earned scores above the 85th %-ile of female scores?
491Male Writing Scores
≈N(491,110)
z.85 1.04score 5021.04(108)score 614.32
85th %-ile for Females
614.32
z 614.32 491
110z 1.12%below .8686
%above .1314
III:Determining Normality• 3a. Did males or females perform better?
Writing400 450 500 550 600 650 700 750 800
SATs Box Plot
Writing400 450 500 550 600 650 700 750 800
SATs Box Plot
The male and female scores are very similar. Both have roughly symmetric distributions with no outliers. The median for females is slightly higher (580 vs 570), but the male average is slightly higher (584.6 vs 580). Both have similar ranges, but the males had slightly more variability in the middle 50%.
III:Determining Normality• 3b. How do the male scores compare with National results?
The males at this school did much better than the overall national mean (584.6 vs. 516). Their scores were also more consistent as evidenced by a lower standard deviation (80.08 vs 115).
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Male400 450 500 550 600 650 700 750 800
SATs Histogram
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Male400 450 500 550 600 650 700 750 800
SATs HistogramSATs
Male
584.5833348
80.0786411.558356
39S1 = meanS2 = countS3 = stdDevS4 = stdErrorS5 = missing count
SATs
Male
584.5833348
80.0786411.558356
39S1 = meanS2 = countS3 = stdDevS4 = stdErrorS5 = missing count
III:Determining Normality• 3c. Are the male and female scores approximately Normal?
The Normal Quantile Plots for both the male and female scores are approximately linear. Therefore, there is evidence that their scores are approximately Normal.
Normal Quantile = -7.3 + 0.0125Male
-2
-1
0
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Male400 450 500 550 600 650 700 750 800
SATs Normal Quantile Plot
Normal Quantile = -7.3 + 0.0125Male
-2
-1
0
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Male400 450 500 550 600 650 700 750 800
SATs Normal Quantile Plot
Normal Quantile = -7.4 + 0.0127Female
-2.5
-2.0-1.5
-1.0-0.5
0.0
0.51.0
1.52.0
2.5
Female400 450 500 550 600 650 700 750 800
SATs Normal Quantile Plot
Normal Quantile = -7.4 + 0.0127Female
-2.5
-2.0-1.5
-1.0-0.5
0.0
0.51.0
1.52.0
2.5
Female400 450 500 550 600 650 700 750 800
SATs Normal Quantile Plot
