Six Metrics, One Family

An online shop tests a redesign on six metrics at once, each with its own hypothesis test:

Running six tests, each at level $\alpha$, lets false alarms pile up, as the ANOVA lesson showed. A multiple-testing correction instead keeps the chance of at least one false rejection across the whole family of $m$ tests at or below $\alpha$. Two common ones:

• Bonferroni: reject a hypothesis when its $p \le \alpha / m$.
• Holm (step-down): sort the p-values from smallest to largest, $p_{(1)} \le p_{(2)} \le \dots \le p_{(m)}$. Compare $p_{(1)}$ with $\alpha/m$, then $p_{(2)}$ with $\alpha/(m-1)$, then $p_{(3)}$ with $\alpha/(m-2)$, and so on: the $k$-th smallest is compared with $\alpha/(m-k+1)$. Reject each one that passes ($p_{(k)} \le$ its threshold), but stop at the first one that fails. That one, and every larger p-value after it, is not rejected.

Holm never rejects fewer hypotheses than Bonferroni, and it keeps the same guarantee.

The analyst cares most about checkout rate. What is the smallest familywise level $\alpha$ at which Holm's procedure declares checkout rate significant?

Round your answer to 4 decimal places.