Question

Problem 2) In absence of special preparation, according to the data from the College Board Web
site, half of students taking the SAT math exam scored above the national average. An educational
researcher was interested in the effectiveness of SAT coaching classes on improving SAT math
scores. Specifically, his study looked at whether a higher proportion of coached students scored
above the national average than for students who had not been coached. He selected a random
sample of 953 students who completed a coaching class prior to taking the SAT math exam and
noted how many scored higher than the national average score for the SAT math exam: 490 did
score higher than the average.
a) Consider just one experimental unit – that is, one student who completed the coaching class
prior to taking the math SAT. What is the response variable for that one student? Categorical or
quantitative?
b) The researcher wants to conduct a significance test to determine if SAT coaching classes are
associated with an increase in the proportion of students who score above the national average.
Verify the conditions for using the normal approximation for the sample proportion.
c) Conduct the significance test. Keep two nonzero digits in your calculation for ??̂ and for the
standard deviation. Sketch the distribution for ??̂ showing mean and area for P-value. State
your conclusion in plain English in the context of the problem. Look at the statements for
Problem 1 and use them as a guide.
d) Based on the conclusion of the significance test, would you recommend an SAT coaching class to
someone taking the SAT math exam? Why?

Answer 1

a)

Whether the student scored higher than the national average score for the SAT math exam or not. It is categorical.

b)

We eneed to test whether half of students taking the SAT math exam scored above the national average. So we have

p = 0.5, n = 953

c)

Conclusion: There is no evidence to conclude that a higher proportion of coached students scored
above the national average than for students who had not been coached.

d)

According to study above it seems coaching is not effective.