Transcript Kevin`s Seminar

Process
• Survey data on 391 students
• Used the Verbal SAT scores
• Processed the information using
MiniTab 15…
Results
• Mean: 591.84
• Standard Deviation: 73.24
Verbal Z-scores
• Took Verbal SAT scores column
• (Verbal SAT - mean) / s.d.
• …created VerbalZ column
-Created histograms comparing the two
Histogram of Verbal SAT scores
• Shows fairly normal shape
• Now, compare it to the histogram
displaying the VerbalZ scores…
• Will it be the same shape?
• Any differences?
What if we superimposed
the VerbalZ histogram over
the Verbal histogram?
• Note the discrepancy between the
two near the mean…
• “The discrepancy has to do with the
choices MiniTab makes about what
interval midpoints to use” - Prof. Pfenning
Count
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<-3
(-3,-2)
(-2,-1)
(-1, 0)
(0,1)
(1,2)
(2,3)
>3
=2/391
=5/391
=47/391
=146/391
=130/391
=49/391
=12/391
=0/391
Proportion of Standardized
Values
• -3 to +3
= .995
• -2 to +2
= .951
• -1 to +1
= .706
Observed vs. Expected
• -3 to +3
= .995 vs .997
• -2 to +2
= .951 vs .95
• -1 to +1
= .706 vs .68
• So… it appears to be fairly normal
90-95-98-99 Rule
• .90 that Z takes a value (-1.645,1.645)
• .95 that Z takes a value (-1.960, 1.960)
• .98 that Z takes a value (-2.326, 2.326)
• .99 that Z takes a value (-2.576, 2.576)
Results for Verbal SATs
• .910 that Z takes a value (-1.645, 1.645)
• .969 that Z takes a value (-2.326, 2.326)
• .979 that Z takes a value (-2.576, 2.576)
- How well does this conform to a perfect curve?