Basic Question for Hypothesis Testing

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

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By lowering the α-value.

Explanation:

The probability of a Type I error is P(Reject H0H0 is true). For example, it’s when the sample mean is significantly different from 0, when the true population mean is not. P(Type I error) for μ is the chance of the true μ lying outside our confidence interval for it, and this is equal to the area under the probability distribution curve outside the C.I. for μ (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 α.

Our α-value is actually set to be equal to the total area in the tail(s). Simply put, that means P(Type I error)=α. Thus, lowering α will mean lowering the chance of Type I error to (100α)%.

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