If it’s relatively riskier to reject the null hypothesis when it might be true, should a smaller or a larger significance level be used?

If it is relatively riskier to reject the null hypothesis when it might be true, a smaller significance level should be used.

Step-by-step explanation:

Rejecting the null hypothesis when it is true is a Type I error.

In hypothesis test, p-value of test statistics is used to compare against significance level.

If p-value < significance level (p-value is smaller than significance level) then the result would be significant and the null hypothesis is rejected.  

To reduce the probability of rejecting the null hypothesis, the chances of the  p-value being smaller than significance level has to be reduced.

For smaller significance level, the chance of p-value < significance level reduces, therefore smaller significance level decreases the risk of the null hypothesis being rejected.

i hope this is what you were looking for.

see attached graph