So, in 1 sample t-test, where null is that mean of sample is zero, I would think a high p-value like 0.30 would imply that null can't be rejected at 5% significance level. However, p-value of 0.012 would imply null will be rejected at 5% significance level but not at 1% significance level.

So, I am confused that 1% being stricter gives low p-value even though high p-value is consider to give us more confidence. Can you guys please explain.

Thanks