In 2000, the mean math SAT score for students at one school was 479. Five years later, in 2005, a teacher performed a hypothesis test to determine whether the average math SAT score of students at the school had changed from the 2000 mean of 479. The hypotheses were
$H_0: \mu = 479$
$H_a: \mu \neq 479$
where $\mu$ is the mean math SAT score, in 2005, for students at the school.
Explain the meaning of a Type I error.
A. A Type I error would occur if, in fact, $\mu = 479$, and the results of the sampling lead to that conclusion.
B. A Type I error would occur if, in fact, $\mu = 479$, but the results of the sampling lead to the conclusion that $\mu \neq 479$
C. A Type I error would occur if, in fact, $\mu = 479$, but the results of the sampling fail to lead to that conclusion.
D. A Type I error would occur if, in fact, $\mu = 479$, but the results of the sampling do not lead to rejection of that fact.
