Answered: The Scholastic Aptitude Test (SAT) is a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The Scholastic Aptitude Test (SAT) is a standardized test for college admissions in the U.S. Scores on the SAT can range from 600 to 2400. Suppose that PrepIt! is a company that offers classes to help students prepare for the SAT exam. In their ad, PrepIt! claims to produce “statistically significant” increases in SAT scores. This claim comes from a study in which 427 PrepIt! students took the SAT before and after PrepIt! classes. These students are compared to 2,733 students who took the SAT twice, without any type of formal preparation between tries.

We also conduct a hypothesis test with this data and find that students who retake the SAT without PrepIt! also do significantly better (p-value < 0.0001). So now we want to determine if PrepIt! students improve more than students who retake the SAT without going through the PrepIt! program.

In a hypothesis test, the difference in sample mean improvement (“PrepIt! gain” minus “control gain”) gives a p-value of 0.004. A 90% confidence interval based on this sample difference is 3.0 to 13.0.

What can we conclude?

The PrepIt! claim of statistically significant differences is valid. PrepIt! classes produce improvements in SAT scores that are 3% to 13% higher than improvements seen in the comparison group.
Compared to the control group, the PrepIt! course produces statistically significant improvements in SAT scores. But the gains are too small to be of practical importance in college admissions.
We are 90% confident that between 3% and 13% of students will improve their SAT scores after taking PrepIt! This is not very impressive, as we can see by looking at the small p-value.

SAT 1ª Try
SAT 2nd Try
Improvement
Mean
Mean
Standard
Mean
Standard
Standard
deviation
deviation
deviation
Preplt!
(n = 427)
Control
500
92
529
97
29
59
506
101
527
101
21
52
(n = 2733)
%3D

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