A p-value of 0.001 indicates that there is a statistically significant association between income and fresh orange juice consumption, which allows us to reject the null hypothesis. However, the p-value does not measure the strength of the association or establish causality.
The student asked about the conclusions that can be drawn from a p-value of 0.001 in the context of a study on income and fresh orange juice consumption. The p-value measures the probability of obtaining the observed results, or more extreme, if the null hypothesis of no effect is true. A p-value of 0.001 is very small, indicating a very low probability that the observed association is due to chance. Therefore, conclusion (1) is correct: The association between income and fresh orange juice consumption is statistically significant. This means we reject the null hypothesis of no association, leading to acknowledgement of a potential relationship between the variables. However, while the p-value can suggest a statistically significant relationship, it does not indicate the strength of such an association, so conclusion (4) is not correct. Moreover, the p-value cannot establish causality, so while conclusion (3) might be true, it cannot be conclusively determined from the p-value alone.