Parents complain that their children do poorly on tests because they don’t spend enough time in the classroom. They claim that every additional hour in school improves the SAT math score by 2 points. You are hired by the Department of Education (DoEd) to investigate this claim. The DoEd has collected data for 96 students from different schools, registering how many hours they spend in the classroom as well as their SAT math scores. Of the 96 students in the dataset, 48 were randomly sampled from schools where students spend 40 hours per week in the classroom, and the average score for these students is 515. The rest of the students were randomly sampled from schools where they spend 45 hours per week in the classroom, and their average score is 525. The sample standard deviation is 23 for the sample of 96 students.
Is the parents’ claim justified?