In addition to being asked about the quality of their sleep the night before the interview survey respondents were asked if they felt ill with headaches felt ill with allergies or felt ill with a cold the day before the interview Gallup provided the following graph based on the responses Did you experience the following feelings during a lot of the day yesterday Percent reporting fair or poor sleep night before Yes experienced illness the day prior No did not experience illness the day prior 46 29 Headaches 37 32 Allergies This graph represents O The conditional distribution of sleep quality given illness experience O The conditional distribution of illness experience given sleep quality O The marginal distribution of illness experience The marginal distribution of sleep quality The joint distribution of sleep quality and mental health state 38 33 Cold Which is a correct interpretation based on this graph O Respondents who experienced headaches during the day were substantially more likely to report fair or poor sleep at night than respondents who did not experience headaches 46 vs 29 O Respondents who reported fair or poor sle night were substantially more likely to have experienced headaches during the day than respondents who did not report fair or poor sleep 46 vs 29 O Respondents who reported fair or poor sleep at night were substantially more likely to have experienced headaches than to not have experienced headaches during the day 46 vs 29