Question 15 • Probability and Statistics with Applications Honors Sem-1-FL-1210300 (2024-2025)
An article in a psychology journal claims that young students who play a musical instrument tend to have higher test scores on state math exams. To assess the claim, a government official considers two methods to collect data.Method 1: Contact many city schools and ask them to provide summary data on state math exam performance and students who participate in music lessons.Method 2: Choose two city schools and provide free music lessons to students who register. At the end of the year, compare state math exam scores for students who participated in the music lessons with the scores for those who did not.
Answer
A
Method 1 is an observational study because past data are collected and analyzed.
B
Method 2 is an observational study because two city schools are chosen to participate.
C
Method 2 is an observational study because students can choose to participate in the music lessons.
D
Both methods are observational studies because both include students who do and do not play a musical instrument.
Explanation
In Method 1, the official only requests existing summary data and does not assign students to take music lessons or otherwise intervene. That makes it an observational study, so choice A is correct. Method 2 provides lessons and compares outcomes, which is an intervention; students choosing whether to register does not make it observational.
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