Question

The Scholastic Aptitude Test (SAT) contains three sections: critical reading, mathematics and writing Each part is scored College Board website. A sample of SAT scores for 5 students follow 500-point scale. Information on test scores for the 2018 version of SAT is available at the on a ANOVA Table SAT scores - 2017 Source of variation Sum of Degrees of Mean F Squares (SS) Square (MS) Student Writing Reading Math freedom 1 453 458 465 2 456 458 459 Treatment 93.3 2.0 46.67 8.75 454 460 457 Error 64,0 12.0 5.33 4. 458 455 461 5 454 454 463 Total 157.3 14 455 457 461 mean allowing for 5% error Conduct a Fisher's LSD test a. b. The level of difficulty for all the three sections of the SAT, measured by the score, are the same. Do you agree with this after the results of the LSD test? WHY supposed to be 寸 n

Answer 1

Answer:

a).

Fisher Pairwise Comparisons

Grouping Information Using the Fisher LSD Method and 95% Confidence

Factor	N	Mean	Grouping
Writing	5	461.00	A
Math	5	457.00		B
Reading	5	455.000		B

Writing is significant with Math and Reading.

b).

We are not agreeing the difficulty is same for all the three. Writing is easy( mean is larger) than Math and Reading.

MINITAB used

One-way ANOVA: Reading, Math, Writing

Method

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor	Levels	Values
Factor	3	Reading, Math, Writing

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	2	93.33	46.667	7.00	0.010
Error	12	80.00	6.667
Total	14	173.33

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
2.58199	53.85%	46.15%	27.88%

Means

Factor	N	Mean	StDev	95% CI
Reading	5	455.000	2.000	(452.484, 457.516)
Math	5	457.00	2.45	(454.48, 459.52)
Writing	5	461.00	3.16	(458.48, 463.52)

Pooled StDev = 2.58199

Fisher Pairwise Comparisons

Grouping Information Using the Fisher LSD Method and 95% Confidence

Factor	N	Mean	Grouping
Writing	5	461.00	A
Math	5	457.00		B
Reading	5	455.000		B

Means that do not share a letter are significantly different.

Fisher Individual Tests for Differences of Means

Difference of Levels	Difference of Means	SE of Difference	95% CI	T-Value	Adjusted P-Value
Math - Reading	2.00	1.63	(-1.56, 5.56)	1.22	0.244
Writing - Reading	6.00	1.63	(2.44, 9.56)	3.67	0.003
Writing - Math	4.00	1.63	(0.44, 7.56)	2.45	0.031

Simultaneous confidence level = 88.44%