Hypothesis Testing and Errors

$\displaystyle H_0$: the new shoe makes no difference to the mean sprint time.
$\displaystyle H_1$: the new shoe changes the mean sprint time.

$\displaystyle 0.014 < 0.05$, so there is sufficient evidence to reject the null hypothesis at the $\displaystyle 5\%$ level.

We never accept the null hypothesis — we only fail to reject it.
The correct conclusion is that there is insufficient evidence to reject the null hypothesis at the $\displaystyle 5\%$ level. That is not the same as proving the soil makes no difference; the test may simply not have detected an effect.

Rejecting the null hypothesis when it is actually true.
Here, concluding that the new battery performs differently when in fact it lasts the same time as the old one.

Failing to reject the null hypothesis when it is actually false.
Here, concluding there is no difference when the new battery really does last a different length of time.

The probability of rejecting the null hypothesis when it is in fact true — that is, the chance of making a Type I error.
At the $\displaystyle 5\%$ level this is $\displaystyle 0.05$.

At the $\displaystyle 5\%$ level: $\displaystyle 0.049 < 0.05$, so reject the null hypothesis.
At the $\displaystyle 1\%$ level: $\displaystyle 0.049 > 0.01$, so there is insufficient evidence to reject the null hypothesis.