In 1990, the average math SAT score for students at one school was 495. Five years later, a teacher wants to perform a hypothesis test to determine whether the average SAT score of students at the
School has changed from the 1990 mean of 495. The hypotheses are: $$\begin{array} { l }
\mathrm { H } _ { 0 } : \mu = 495 \
\mathrm { H } _ { \mathrm { a } } : \mu \neq 495
\end{array}$$
Explain the meaning of a Type II error.
A) Concluding that $\mu \neq 495$ minutes when in fact $\mu = 495$
B) Failing to reject the hypothesis that $\mu = 495$ when in fact $\mu = 495$
C) Failing to reject the hypothesis that $\mu = 495$ when in fact $\mu \neq 495$
D) Concluding that $\mu 495$ when in fact $\mu = 495$

Question

In 1990, the average math SAT score for students at one school was 495. Five years later, a teacher wants to perform a hypothesis test to determine whether the average SAT score of students at the
School has changed from the 1990 mean of 495. The hypotheses are: $$\begin{array} { l } 
\mathrm { H } _ { 0 } : \mu = 495 \
\mathrm { H } _ { \mathrm { a } } : \mu \neq 495
\end{array}$$
Explain the meaning of a Type II error.
A) Concluding that $\mu \neq 495$ minutes when in fact $\mu = 495$
B) Failing to reject the hypothesis that $\mu = 495$ when in fact $\mu = 495$
C) Failing to reject the hypothesis that $\mu = 495$ when in fact $\mu \neq 495$
D) Concluding that $\mu > 495$ when in fact $\mu = 495$

Quizplus · Accepted Answer

A Type II error occurs when we fail to reject the null hypothesis when it is actually false. In this context, it means failing to reject the hypothesis that the average SAT score is 495 when it is actually different from 495.

In 1990, the Average Math SAT Score for Students at One