Any help will be appreciated! thank you so much! Question 3: Suppose that we est

Question

Any help will be appreciated! thank you so much!

Question 3: Suppose that we estimate the following relationship between test scores in math and class size (where the bracketed numbers below denote standard errors): mathscore 424 -5.4classsize, (58.5) (2.9) Part (a): Test whether class size has a statistically significant effect on math scores at the 10% level of significance. Part (b): A school-grade has an average class size of 32 students. What is its expected average test score? Part (c): A classroom currently has 32 students and one teacher. The principal is won dering whether it is worth hiring another teacher (to create two classrooms of 16 students) The teacher salary is $50,000. The principal values each one unit increase in average test scores at $500. Should the principal hire the additional teacher?

Explanation / Answer

a) TS = -5.4 / 2.9 = -1.862068
at 10 % ,
you have not provided sample size ,i am assuming it is large enough
hence t-critical = 1.645
since |TS| > t-critical
we reject the null and conclude that class size has significant effect
b)
y^ = 424 - 5.4 * class_size
= 424 - 5.4 * 32
= 251.2

c)
if class size = 16
score increase by 16 *5.4 = 86.4

cost for 86.4 = 86.4 * 500 = 43200

since 500000> 43200
the principle should not hire additional teacher

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