(Round intermediate calculations to at least 4 decimal places.) The SAT has gone
ID: 3324747 • Letter: #
Question
(Round intermediate calculations to at least 4 decimal places.)
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 (Washington Post, August 30, 2006). Consider the following portion of data on 20 students who took the SAT last year. Information includes each student’s score on the writing and math sections of the exam. Also included are the student’s GPA and the values of a Gender dummy variable with 1 for females and 0 for males.
Estimate a linear regression model with Writing as the response variable and GPA and Gender as the explanatory variables. (Round your answers to 2 decimal places.)
Compute the predicted writing score for a male student with a GPA of 3.5. Repeat the computation for a female student. (Round your answers to 2 decimal places.)
Select the null and the alternative hypotheses to test if there is a gender difference in writing scores.
Can we conclude that there is a statistically significant gender difference in writing scores at a 5% level?
(Round intermediate calculations to at least 4 decimal places.)
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 (Washington Post, August 30, 2006). Consider the following portion of data on 20 students who took the SAT last year. Information includes each student’s score on the writing and math sections of the exam. Also included are the student’s GPA and the values of a Gender dummy variable with 1 for females and 0 for males.
Explanation / Answer
a] Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 316.4 32.9 9.62 0.000
GPA 81.7 10.9 7.49 0.000 1.03
Gender 16.59 9.17 1.81 0.088 1.03
Regression Equation
Writing = 316.4 + 81.7 GPA + 16.59 Gender
b] GPA = 3.5 Female =1 Male = 0
Writing = 316.4 + 81.7 * 3.5 + 16.59 * 1
Writing = 618.94
Writing = 316.4 + 81.7 *3.5 + 16.59 *0
Writing = 602.35
Male student = 602.35
Female student = 618.94
c 1 ] null and the alternative hypotheses
H0: 2 = 0; HA: 2 0
c 2 ] pvalue = 0.088 > alpha = 0.05
No, since we do not reject H0.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.