A school compares the mean number of minutes of homework completed per night for students using a planner app (Group A) versus students not using it (Group B). The researchers report a 95% confidence interval for of minutes and claim that planner-app users complete more homework on average. Is the claim supported by the interval?
- No, because 0 is not in the interval, so there is no difference.
- Yes, because the entire interval is above 0, supporting that . (correct answer)
- No, because the interval is for , not .
- Yes, because 95% of students in Group A did more homework than 95% of students in Group B.
- Yes, because the interval proves planner-app use causes more homework to be completed.
Explanation: This question tests understanding of confidence intervals for comparing two means. The 95% confidence interval for μ_A - μ_B is (4.2, 12.8), which means we're 95% confident the true difference in mean homework minutes (planner app users minus non-users) lies between 4.2 and 12.8 minutes. Since the entire interval is above 0, this supports the claim that μ_A > μ_B. Choice A incorrectly interprets 0 not being in the interval as meaning there's no difference, when actually it means there IS a difference. Choice C confuses the order of subtraction. Choice D misinterprets the interval as describing individual students rather than population means. Choice E incorrectly claims causation from an observational study. When a confidence interval for μ_1 - μ_2 is entirely positive, it supports the claim that μ_1 > μ_2.