help stats Q 3) The Scholastic Aptitude Test (SAT) contains three sections: crit
ID: 3303449 • Letter: H
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help stats Q
3) The Scholastic Aptitude Test (SAT) contains three sections: critical reading, mathematics and writing Each part is scored on a 500-point scale. Information on test scores for the 2015 version of SAT is available at the College Board website. A sample of SAT scores for 5 students follow: ANOVA Table Source ofSum ofDegreesMean variation Squares of Square (SS)freedom (MS) 2.0 12.0 Treatment 63.3 31.6710.33 Error 36.8 3.07 Total 100.1 SAT scores 2014 Student Reading MathWriting 453 456 454 458 454 455 458 459 460 456 457 458 461 459 457 460 463 460 3 5 mean a. Conduct a Fisher's LSD test allowing for 5% error. b. The level of difficulty for all the three sections of the SAT, measured by the score, are supposed to be the same. Do you agree with this after the results of the LSD test? WHY?Explanation / Answer
The data is copied in Excel as given.
Student
Reading
Math
Writing
1
453
458
461
2
456
459
459
3
454
460
457
4
458
456
460
5
454
457
463
a)
Go to Data tab -> Click on Data Analysis toolpack -> Choose Anova : Single Factor -> Click OK.
In the input range box, select the cells containing just the values with labels and tick the label box. By default, the separator is chosen as columns, so no need to alter.
Click OK.
The following result is obtained :
Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
Reading
5
2275
455
4
Math
5
2290
458
2.5
Writing
5
2300
460
5
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
63.33333
2
31.66667
8.26087
0.005547
3.885294
Within Groups
46
12
3.833333
Total
109.3333
14
LSD critical value = t0.05;dfe * (MSW*2/n) ,
since all the sample sizes are same (n=5), where MSW = 3.83333 and dfe = 12.
LSD critical value = 2.697977, where t0.05;12 = 2.178813.
[To find t0.05;12 , type “=T.INV.2T(0.05,12)” and press Enter.]
Now we compare the absolute differences of the means of the groups with the critical value.
If the absolute mean difference between two groups > critical value, there is significant difference between the two particular groups else no significant difference.
Absolute mean differences are given :
LSD(reading,math)
3
>Critical value
LSD(writing,math)
2
<critical value
LSD(reading,writing)
5
>critical value
Here, we observe that there is significant difference between reading and math scores and between reading and writing scores at 5% level.
b) No, I don’t agree with this since from the LSD test, we obtained the conclusion that there is significant difference between reading and math scores and between reading and writing scores.
Student
Reading
Math
Writing
1
453
458
461
2
456
459
459
3
454
460
457
4
458
456
460
5
454
457
463
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