Question

A new online test preparation company compared 3,025 students who had not used its program with 2,150 students who had. Of those students who did not use the online test preparation program, 1,513 increased their scores on the SAT examination compared with 1,100 who did use the program. A significance test was conducted to determine whether there is evidence that the online test preparation company's students were more likely to increase their scores on the SAT exam. What is the p-value for an appropriate hypothesis test?

a. 0

b. 0.2082

c. 0.4164

d. 0.7198

e.1

Answer 1

Sample 1: Students who had not used new online test preparation company program

Sample 2 : Students who had used new online test preparation company program

p₁ : Proportion of students who had not used new online test preparation company program increased their scores on the SAT exam

p₂: Proportion of students who had used new online test preparation company program increased their scores on the SAT exam

Claim : online test preparation company's students were more likely to increase their scores on the SAT exam

i.e p₁ < p₂ of p₁ -p₂ < 0

Null hypothesis : H_o : p₁ -p₂ = 0

Alternate Hypothesis : H_a : p₁ -p₂ < 0

Left Tailed test:

Number Students who had not used new online test preparation company program: n₁ = 3025

Number Students who had not used new online test preparation company program,increased their scores on the SAT examination :x₁ = 1513

Number Students who had used new online test preparation company program: n₂= 2150

Number Students who had used new online test preparation company program,increased their scores on the SAT examination :x₂ = 1100

Sample Proportion of students who had not used new online test preparation company program increased their scores on the SAT exam:

=x₁/n₁=  1513/3025= 0.5002

Sample Proportion of students who had used new online test preparation company program increased their scores on the SAT exam:

= x₂/n₂ = 1100/2150 = 0.5116

For left tailed test :

Answer :

b. 0.2082