75 % level of significance means there are _____ out of 100 chances of committing type I errora.25b.75c.7.5d.0.75

Breakdown the Problem

1. We need to understand what a 75% level of significance means in the context of hypothesis testing and Type I error.

Relevant Concepts

2. The level of significance (denoted as α) is the probability of making a Type I error, which is rejecting the null hypothesis when it is true. A 75% level of significance indicates that there is a 75% chance of making this error.

Analysis and Detail

3. Since a 75% significance level means that we are willing to accept a 75% chance of a Type I error, this can be restated in terms of the chance of not making an error:
   • $100\% - 75\% = 25\%$
4. Thus, the correct interpretation is that there are 25 chances out of 100 of committing a Type I error.

Verify and Summarize

5. Most commonly:
   • Level of significance (α) = 75% means there are 75 chances out of 100 of incorrectly rejecting the null hypothesis.
   • Therefore, the chance of committing a Type I error is indeed 25 out of 100.

Final Answer

The answer is a. 25.