Consider the following SAT scores on the math and verbal portions of SAT-1, which are based on reported statistics from the College Board.

Verbal Math

Female 646 539 348 623 478 484 489 436 396 545

429 298 782 626 533 504 574 352 365 350

Male 562 525 512 576 570 547 678 464 651 645

480 571 555 519 596 673 624 624 328 548

Using a 0.05 significance level and the computer output provided below, answer the following questions related to these data.

Dependent Variable: score

Sum of

SourceDFSquaresMean SquareF ValuePr > F

Model390190.275030063.42502.870.0496

Error36376748.100010465.2250

Corrected Total39466938.3750

R-SquareCoeff VarRoot MSEscore Mean

0.19315219.44399102.2997526.1250

SourceDFType III SSMean SquareF ValuePr > F

gender152635.0250052635.025005.030.0312

test16027.025006027.025000.580.4529

gender*test131528.2250031528.225003.010.0912

Standard

ParameterEstimateErrort ValuePr > |t|

Intercept546.6000000 B32.3500000016.90<.0001

genderFemale-16.4000000 B45.74980874-0.360.7221

genderMale0.0000000 B...

testMath31.6000000 B45.749808740.690.4942

testVerbal0.0000000 B...

gender*test Female Math-112.3000000 B64.70000000-1.740.0912

gender*test Female Verbal0.0000000 B...

gender*test Male Math0.0000000 B...

gender*test Male Verbal0.0000000 B...

a.Test the null hypothesis that SAT scores are not affected by an interaction between gender and test (verbal/math). What do you conclude?

b.Assume that SAT scores are not affected by an interaction between gender and type of test (verbal/math). Is there sufficient evidence to support the claim that gender has an effect on SAT scores? Note: Technically, at this point, we should refit a new model with the interaction removed. For the purpose of this problem, however, you just need to select the most appropriate test statistic and p-value from the given output.

c.Assume that SAT scores are not affected by an interaction between gender and type of test (verbal/math). Is there sufficient evidence to support the claim that type of test (verbal/math) has an effect on SAT scores? Note: Technically, at this point, we should refit a new model with the interaction removed. For the purpose of this problem, however, you just need to select the most appropriate test statistic and p-value from the given output.

d.How would you write the ANOVA model given in the output above?