# Hypothesis Test Q

Hey guys, just wanted some confirmation/explaination… So it’s my understanding that as the significance level decreases (ie. from 0.5 to 0.1), the chance of accepting a null hypothesis increases? I thought if you specify a smaller significance level you are being more precise and there is less of a chance of accepting a null hypothesis? Thanks

there is less chance of REJECTING A NULL

look at the width of the confidence interval - which is the acceptance region for the null. everything below is for a two-tailed test. at 0.05 Level of significance - you have +/- 1.96 std deviations (assuming a normal distribution) = total area of 3.92 std. deviations from the mean as the acceptance region. at 0.01 level of significance you have +/- 2.58 std. deviations (total area = 5.16 std deviations from the mean as the acceptance region. so as level of significance decreases - area for acceptance increases.

Yeah okay, that makes sense now, the small the significance level specified the less chance of rejecting a null hypth… thanks!