Which statement correctly represents the null hypothesis in the height and prostate cancer risk scenario?

• A. Taller men have greater risk for prostate cancer than shorter men
• B. There is a threshold effect where only very tall men have increased risk
• C. Height is not associated with prostate cancer risk in any subgroup
• D. There is no difference in prostate cancer risk between taller and shorter men

Answer: (D)

In hypothesis testing, the null hypothesis is a statement of no association or no difference between groups. For height and prostate cancer risk, the null would say that height is not related to risk, meaning taller and shorter men have the same risk. That’s exactly what the option describing no difference between taller and shorter men states. Other statements propose specific patterns of association—like a directional increase with height, a threshold effect, or subgroup-specific results—which are not the general null. Thus, the null hypothesis is that there is no difference in prostate cancer risk between taller and shorter men.