Sepsis occurs when a person's body has an overwhelmingly dangerous response to an infection. It can affect people of all ages and is life-threatening. Because vitamin C is believed to reduce inflammation, a randomized experiment was designed to see if intravenous administration of high-dose vitamin C would improve outcomes in patients with sepsis. Half the patients received an infusion of vitamin C while the other half received a placebo infusion.

(a) Over a follow-up period of 28 days, the mean number of days on a ventilator was not significantly different between the two groups, while the mean number of days out of the Intensive Care Unit was significantly different. The p-values for these two tests were 0.03 and 0.15. Which p-value goes with which test?

(b) Part (a) describes one test that was significant and one that wasn't in this study. In fact, many outcomes were measured and forty-six different tests were conducted. Forty-three of the 46 tests did not show a significant difference between the vitamin C group and the placebo group, while 3 did show significance at the 5% level. Explain why we should hesitate to attach too much importance to the three significant results.