# How can the probability of a type I error be reduced?

By lowering the $\alpha$-value.
The probability of a Type I error is $P \left(\text{Reject "H_0|H_0" is true}\right)$. For example, it's when the sample mean is significantly different from 0, when the true population mean is not. $P \left(\text{Type I error}\right)$ for $\mu$ is the chance of the true $\mu$ lying outside our confidence interval for it, and this is equal to the area under the probability distribution curve outside the C.I. for $\mu$ (e.g. the left and right tails).
The chance of a Type I error occurring is directly related to the width of our C.I. for the parameter. If we want to decrease the chance of Type I error, we increase the width of the C.I., which means decreasing the area we wish to have in the tails, and that is simply done by decreasing the value we use for $\alpha$.
Our $\alpha$-value is actually set to be equal to the total area in the tail(s). Simply put, that means $P \left(\text{Type I error}\right) = \alpha$. Thus, lowering $\alpha$ will mean lowering the chance of Type I error to (100 * alpha)%.