7. Are the drugs really effective? A March 29, 2012, article in the Columbus Dispatch reported that a former researcher at a major pharmaceutical company found that many basic studies on the effectiveness of new cancer drugs appeared to be unreliable. Among the studies the former researcher reviewed was one that had been published in a reputable journal. In this published study, a cancer drug was reported as having a statistically significant positive effect on treating cancer. For purposes of this problem, assume that statistically significant means significant at level 0.05.

(a) Explain in language that is understandable to someone who knows no statistics what "statistically significant at level 0.05" means.

(b) The former researcher interviewed the lead author of the published paper. The newspaper article reported that the lead author admitted that they had repeated their experiment six times and got a significant result only once, but put it in the paper because it made the best story. In light of this admission, do you think that it is accurate to claim in their published study that the findings were significant at the 0.05 level? Explain your answer. (Note: A statistician can show that an event that has only probability 0.05 of occurring on any given trial will occur at least once in six trials with probability about 0.26.)