[original post removed]
Type I error: incorrect rejection of a true null hypothesis (also known as a “false positive” finding)
You had a band mu +/- 2.2 --> due to original band setting
if mu was 10 e.g. - you said something was NOT in the range - when the measure for that item was say 12.25 - because it was beyond 12.2
when you widen the band - it becomes e.g. 10+/- 2.5 … and now 12.25 is within the band. and hence acceptable.