3) Does school size affect student test scores? We can test this question empiri

Question

3) Does school size affect student test scores? We can test this question empirically by estimating the following regression equation: where, score the average score of 10 graders in a standardized math test in high school i. avgcomp- is the average salary (in dollars) of teachers in high school i. staff- the number of teachers (per thousand students) in high school i. enrollment-the number of students in high school i. a) What is the expected sign of the coefficient on avgcomp? Explain why b) A Senator argues that the more teachers per student, then the more personalized is education and the better the leaming of students. i) What is the expected sign of the coefficient ofsty? ii) Write the null and alternative hypothesis for this question. c) The senator also argues that larger schools may lose the sense of community which may reduce faculty commitment, makes faculty-principal communication more impersonal and difficult, and increases the complexity of the school administration including the supervision of teachers and the evaluation of their teaching effectiveness. Consequently student performance is negatively affected by school size. i) What is the expected sign of the coefficient of enrollment? ii) Write the null and alternative hypothesis for this question.

Explanation / Answer

a) the expected sign on avgcomp is positive because when the salary of the teachers increase , they become more incentivised to improve their teaching and hence there will be an improvement in test scores.

b) i) The expected sign of the coefficient is positive because as more number of teachers leads to more personalised attention and hence improvement in student learning leading to better scores

ii) Null hypotheis : B2 = 0

Alternate hypothesis : B2 =/( is not equal to) 0

c) i) The expected sign of enrollment would be negative as larger schools induce lower student outcomes as per the senator

ii) Null Hypothesis : B3 = 0

Alternate Hypothesi : B3 =/(is not equal to ) 0

d) i) The coefficient on staff is 0.048 which implies that with an increase in staff by one teacher, the student score would increase by 0.048 i.e the contribution of one additional teacher to the student outcome is 0.048

ii) The p value of the coefficient is 0.040 and hence the coefficient is statistically significant at 5 % level of significance and the null hypothesis is not rejected

iii) Yes it is true that teachers per student improve performance as students get more attention and supervision

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