Round intermediate calculations to at least 4 decimal places.) The SAT has gone
ID: 3314750 • Letter: R
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 t 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 O for males he usual WritingMathGPAGender 620 570 0 2 570 620 570 3.39 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.) Math GPA + Female a-2. Compute the predicted math score for a male and female student with a GPA of 3.5. (Round your final answers to 2 decimal places.) Math Male student Female student b-1. Select the null and the alternative hypotheses to test if there is a gender difference in math scores b-2 Can we conclude that there is a statistically significant gender difference in math scores at the 5% level? O Yes, since we reject Ho O Yes, since we do not reject Ho O No, since we reject Ho No, since we do not reject HoExplanation / Answer
a-1) The regression equation is
Math = 274 + 98.7 GPA - 21.1 Female
a-2) If GPA = 3.5 and Male student
Math = 274 + 98.7 (3.5) - 21.1 (0) = 619.45
If GPA = 3.5 and Female student
Math = 274 + 98.7 (3.5) - 21.1 (1) = 598.35
b-1) Correct answer: option (C)
b-2)
Correct answer: option (D)
since
Predictor Coef SE Coef T P
Constant 274.12 37.85 7.24 0.000
GPA 98.71 12.54 7.87 0.000
Female -21.10 10.55 -2.00 0.062
Here P-value > alpha 0.05, so we accept H0. i.e. no significant
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.