Question

Preventing colds A medical experiment investigated whether taking the herb echinacea could help prevent colds. The study measured $50$ different response variables usually associated with colds, such as low-grade fever, congestion, frequency of coughing, and so on. At the end of the study, those taking echinacea displayed significantly better responses at the$\alpha =0.05$ level than those taking a placebo for $3$ of the $50$ response variables studied. Should we be convinced that echinacea helps prevent colds? Why or why not?

Short answer

There isn't enough evidence to establish that Echinacea is helpful in preventing colds.

Step-by-step solution

Given information

$\alpha =0.05$

Calculation

To conclude that Echinacea is useful, there is insufficient evidence. The substantial results for the three variables are almost certainly coincidental.

When the null hypothesis is true $5\%$of the time, there is a type $I$error getting a significant result at the $\alpha =0.05$level.

If $50t-$tests are run at this level of significance and all $50$null hypotheses are true, the average Type $I$error is $0.05\times 50=2.5$

The three most important findings Such errors are very likely to occur in this setting.