You are conducting a one-way analysis of variance to compare the population means of four independent groups. given that all means are equal in the population, what is the probability that the null hypothesis will be rejected denoted by?

a. α
b. β
c. 1-α
d. 1- β

So on this case we are assuming that we reject a true null hypothesis. And that's defined as a Type of Error I.

And the probability to commit Type of error I is denoted by

So on this case the best answer is:

A. α

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"  

Type I error is "the rejection of a true null hypothesis  "false positive "conclusion".

Type II error is "the non-rejection of a false null hypothesis "false negative" conclusion"

Solution to the problem

On this case the syatem of hypothesis that we are trying to check are:

Null hypothesis:

Alternative hypothesis: Not all the means are equal    i,j=1,2,3,4

For this case we want to answer this question: "Given that all means are equal in the population, what is the probability that the null hypothesis will be rejected denoted by?"

So on this case we are assuming that we reject a true null hypothesis. And that's defined as a Type of Error I.

And the probability to commit Type of error I is denoted by

So on this case the best answer is:

A. α

right

step-by-step explanation: