AP Statistics · Question of the Day

AP Statistics Question of the Day

A fresh daily question to build accuracy, reinforce recall, and turn practice into a steady habit.

Monday, September 21, 2026

A botanist measures $n=25$ plants of the same species and uses linear regression to predict plant height ( $y$ , cm) from hours of sunlight per day ( $x$ ). The botanist claims that, in the population, additional sunlight increases average height, so the population regression slope is positive. Which hypotheses are appropriate for testing this claim about the slope?

Keep practicing AP Statistics

Question of the Day

Answer today's AP Statistics question, reveal the full explanation, then keep the streak going with a new question every day.

$H_0: r=0$ vs. $H_a: r>0$
$H_0: \beta=0$ vs. $H_a: \beta>0$ (correct answer)
$H_0: b=0$ vs. $H_a: b>0$
$H_0: \beta\ne 0$ vs. $H_a: \beta=0$
$H_0: \beta=0$ vs. $H_a: \beta\ne 0$

Explanation: The botanist claims additional sunlight increases plant height, indicating a positive slope in the population regression model. This directional claim requires a one-sided test with the alternative hypothesis showing β > 0. Choice B correctly sets up H₀: β = 0 (no linear relationship) versus Hₐ: β > 0 (positive relationship), using the population parameter β. Choice C incorrectly uses sample slope b, while choice A uses correlation r. Choice E would be appropriate for a two-sided test but doesn't match the directional claim. When a researcher makes a specific directional claim about increase or decrease, the alternative hypothesis must reflect that direction using the appropriate inequality.