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Which of the following is a Type I​ error?

A. The president fails to reject the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.398​, ​when, in​ fact, the proportion is 0.398.
B. The president rejects the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.398​, ​when, in​ fact, the proportion is less than 0.398.
C. The president rejects the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.398​, ​when, in​ fact, the proportion is 0.398.
D. The president fails to reject the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.398​, ​when, in​ fact, the proportion is less than 0.398.

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Answer:

C. The president rejects the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.398​, ​when, in​ fact, the proportion is 0.398.

Step-by-step explanation:

A type I error occurs if you reject the null hypothesis when it is true.

Now the hypotheses are:

[tex]H_0:[/tex] The proportion is 0.398

[tex]H_1:[/tex] The proportion is less than 0.398

If in actual fact the proportion is 0.398, then the president must not reject the [tex]H_0[/tex].

This is a correct decision.

If in actual fact the proportion is 0.398, and the president rejects the [tex]H_0[/tex], then a type I error is committed.

The correct choice is C.

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