Question

Q1. The quantitative reasoning scores on the GRE were recorded for students admitted to three different...

Q1. The quantitative reasoning scores on the GRE were recorded for students admitted to three different graduate programs as below.

(a): Construct an ANOVA table for the data using Completely Randomized Design?

(b): If you find a significant difference in the average scores for the three programs, Use Tukey’smethod for paired comparisons to determine which means differ significantly. Use α = .05.

  Life   

Physical    

Social

630

660

440

640

640

330

470

720

670

600

690

570

580

530

590

660

760

540

660

670

4 50

480

700

570

650

710

530

710

450

630

Homework Answers

Answer #1
Life Physical Social Total
Sum 6080 6530 5320 17930
Count 10 10 10 30
Mean, Sum/n 608 653 532
Sum of square, Ʃ(xᵢ-x̅)² 55360 79610 90960

a) Null and Alternative Hypothesis:

Ho: µ1 = µ2 = µ3

H1: At least one mean is different.

Number of treatment, k = 3

Total sample Size, N = 30

df(between) = k-1 = 2

df(within) = N-k = 27

df(total) = N-1 = 29

SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 - (Grand Sum)²/ N = 74806.6667

SS(within) = SS1 + SS2 + SS3 = 225930

SS(total) = SS(between) + SS(within) = 300736.6667

MS(between) = SS(between)/df(between) = 37403.3333

MS(within) = SS(within)/df(within) = 8367.7778

F = MS(between)/MS(within) = 4.4699

p-value = F.DIST.RT(4.4699, 2, 27) = 0.0210

Decision:

P-value < α, Reject the null hypothesis.

ANOVA
Source of Variation SS df MS F P-value
Between Groups 74806.6667 2 37403.3333 4.4699 0.0210
Within Groups 225930.0000 27 8367.7778
Total 300736.6667 29

b) At α = 0.05, k = 3, N-K = 27, Q value = 3.51

HSD = 3.51*√(8367.7778/10) = 101.5342

Comparison Diff. = (xi - xj) HSD Results
x̅1-x̅2 -45 101.5342 Means are not different
x̅1-x̅3 76 101.5342 Means are not different
x̅2-x̅3 121 101.5342 Means are different
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