Questions: Select the appropriate word or phrase to complete the sentence. If we decrease the value of the significance level α, we (Choose one) τ the probability of a Type I error.

Select the appropriate word or phrase to complete the sentence.

If we decrease the value of the significance level α, we (Choose one) τ the probability of a Type I error.

Transcript text: Select the appropriate word or phrase to complete the sentence. If we decrease the value of the significance level $\alpha$, we (Choose one) $\tau$ the probability of a Type I error.

Solution

Solution Steps

Step 1: Understanding the significance level and Type I error

The significance level, denoted by $\alpha$, is the probability of rejecting the null hypothesis when it is actually true. This is also known as a Type I error. A Type I error occurs when we incorrectly conclude that there is an effect or difference when there is none.

Step 2: Analyzing the relationship between $\alpha$ and Type I error

If we decrease the value of $\alpha$, we are reducing the threshold for rejecting the null hypothesis. This means that we are less likely to reject the null hypothesis when it is true, thereby decreasing the probability of a Type I error.

Step 3: Completing the sentence

The sentence states: "If we decrease the value of the significance level $\alpha$, we (Choose one) $\tau$ the probability of a Type I error." Based on the analysis, the appropriate word to complete the sentence is "decrease."

Final Answer

\$\boxed{\text{decrease}}\$

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