The SAT has gone through many revisions over the years. In 2005, a new writing s
ID: 3058675 • Letter: T
Question
The SAT has gone through many revisions over the years. In 2005, a new writing section was introduced that includes a direct writing measure in the form of an essay. People argue that female students generally do worse on math tests but better on writing tests. Therefore, the new section may help reduce the usual male lead on the overall average SAT score (The Washington Post, August 30, 2006). Consider the following data on 20 students who took the SAT test last year. Information includes each student’s score on the math and writing sections of the exam. Also included are the student’s GPA and a dummy that equals 1 for female and 0 for male.
Writing
Math
GPA
Female
501
614
2.63
0
595
626
3.36
1
482
516
3.13
0
529
659
2.97
0
494
601
2.72
0
503
510
3.25
0
549
562
2.45
0
598
621
2.54
1
603
545
2.46
0
582
550
3.17
1
594
616
2.66
0
505
562
3.48
0
634
597
2.81
1
497
514
3.04
1
589
531
2.97
0
524
567
2.96
1
620
552
3.04
1
579
582
3.05
0
523
510
2.91
1
583
600
2.89
1
Click here for the Excel Data File
a-1.
Estimate a linear regression model with math score as the response variable and GPA and the female dummy variable as the explanatory variables. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
= + GPA + Female.
a-2.
Compute the predicted score for a male and female student with a GPA of 3.3. (Round your intermediate coefficient values and final answers to 2 decimal places.)
Male student
Female student
b-1.
Select the null and the alternative hypotheses to test if there is a gender difference in writing scores.
H0: 2 = 0; HA: 2 0
H0: 2 = 0; HA: 2 < 0
H0: 2 = 0; HA: 2 > 0
b-2.
Can we conclude that there is a statistically significant gender difference in math scores at the 5% level?
Yes, since we reject H0.
Yes, since we do not reject H0.
No, since we reject H0.
No, since we do not reject H0
The SAT has gone through many revisions over the years. In 2005, a new writing section was introduced that includes a direct writing measure in the form of an essay. People argue that female students generally do worse on math tests but better on writing tests. Therefore, the new section may help reduce the usual male lead on the overall average SAT score (The Washington Post, August 30, 2006). Consider the following data on 20 students who took the SAT test last year. Information includes each student’s score on the math and writing sections of the exam. Also included are the student’s GPA and a dummy that equals 1 for female and 0 for male.
Explanation / Answer
The SAT has gone through many revisions over the years. In 2005, a new writing section was introduced that includes a direct writing measure in the form of an essay. People argue that female students generally do worse on math tests but better on writing tests. Therefore, the new section may help reduce the usual male lead on the overall average SAT score (The Washington Post, August 30, 2006). Consider the following data on 20 students who took the SAT test last year. Information includes each student’s score on the math and writing sections of the exam. Also included are the student’s GPA and a dummy that equals 1 for female and 0 for male.
Writing
Math
GPA
Female
501
614
2.63
0
595
626
3.36
1
482
516
3.13
0
529
659
2.97
0
494
601
2.72
0
503
510
3.25
0
549
562
2.45
0
598
621
2.54
1
603
545
2.46
0
582
550
3.17
1
594
616
2.66
0
505
562
3.48
0
634
597
2.81
1
497
514
3.04
1
589
531
2.97
0
524
567
2.96
1
620
552
3.04
1
579
582
3.05
0
523
510
2.91
1
583
600
2.89
1
Click here for the Excel Data File
a-1.
Estimate a linear regression model with math score as the response variable and GPA and the female dummy variable as the explanatory variables. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
= + GPA + Female.
a-2.
Compute the predicted score for a male and female student with a GPA of 3.3. (Round your intermediate coefficient values and final answers to 2 decimal places.)
Male student
Female student
b-1.
Select the null and the alternative hypotheses to test if there is a gender difference in writing scores.
H0: 2 = 0; HA: 2 0
H0: 2 = 0; HA: 2 < 0
H0: 2 = 0; HA: 2 > 0
b-2.
Can we conclude that there is a statistically significant gender difference in math scores at the 5% level?
Yes, since we reject H0.
Yes, since we do not reject H0.
No, since we reject H0.
No, since we do not reject H0
The SAT has gone through many revisions over the years. In 2005, a new writing section was introduced that includes a direct writing measure in the form of an essay. People argue that female students generally do worse on math tests but better on writing tests. Therefore, the new section may help reduce the usual male lead on the overall average SAT score (The Washington Post, August 30, 2006). Consider the following data on 20 students who took the SAT test last year. Information includes each student’s score on the math and writing sections of the exam. Also included are the student’s GPA and a dummy that equals 1 for female and 0 for male.
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