The SAT Reasoning Test is an exam taken by most high school students as part of their co...

The SAT Reasoning Test is an exam taken by most high school students as part of their college admission requirements. A proposal has been made to alter the exam by having the students take the exam on a computer. The exam questions would be selected for the student in the following fashion. For a given section of questions, if the student answers the initial questions posed correctly, then the following questions become increasingly difficult. If the student provides incorrect answers for the initial questions asked in a given section, then the level of difficulty of latter questions does not increase. The final score on the exams will be standardized to take into account the overall difficulty of the questions on each exam. The testing agency wants to compare the scores obtained using the new method of administering the exam to the scores using the current method. A group of 182 high school students is randomly selected to participate in the study with 91 students randomly assigned to each of the two methods of administering the exam. The data are summarized in the following table and boxplots for the math portion of the exam.

Evaluate the two methods of administering the SAT exam. Provide tests of hypotheses and confidence intervals. Are the means and standard deviations of scores for the two methods equivalent? Justify your answer using α = .05 .