A study conducted on a college campus tested to see whether students with colds who are given large doses of vitamin C recover faster than students who are not given the vitamin C. The p-value for the test is 0.003.

(a) Given the p-value, what is the conclusion of the test: Reject H₀ or do not reject H₀?
(b) Results of statistical inference are only as good as the data used to obtain the results. No matter how low a p-value is, it has no relevance (and we can’t trust conclusions from it) if the data were collected in a way that biases the results. Describe an inappropriate method of collecting the data for this study that would bias the results so much that a conclusion based on the p-value is very unreliable.
(c) Describe a method of collecting the data that would allow us to interpret the p-value appropriately and to extend the results to the broader student population.
(d) Assuming the data were collected as you describe in part (c), use the p-value to make a conclusion about vitamin C as a treatment for students with a common cold.