In 2014 , the average math SAT score for students at one school was 472 . 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 2014 mean of 472 . The hypotheses are:
$\begin{array} { l }
H _ { 0 } : \mu = 472 \
H _ { A } : \mu \neq 472
\end{array}$
Explain the result of a Type II error.
A) The teacher will conclude that the mean math SAT score at the school is the same when in fact it is the same.
B) The teacher will conclude that the mean math SAT score at the school has increased when in fact it is the same.
C) The teacher will conclude that the mean math SAT score at the school is different when in fact it is the same.
D) The teacher will conclude that the mean math SAT score at the school has decreased when in fact it is the same.
E) The teacher will conclude that the mean math SAT score at the school is the same when in fact it is different

Question

In 2014 , the average math SAT score for students at one school was 472 . 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 2014 mean of 472 . The hypotheses are:
$\begin{array} { l } 
H _ { 0 } : \mu = 472 \
H _ { A } : \mu \neq 472
\end{array}$
Explain the result of a Type II error.
A) The teacher will conclude that the mean math SAT score at the school is the same when in fact it is the same.
B) The teacher will conclude that the mean math SAT score at the school has increased when in fact it is the same.
C) The teacher will conclude that the mean math SAT score at the school is different when in fact it is the same.
D) The teacher will conclude that the mean math SAT score at the school has decreased when in fact it is the same.
E) The teacher will conclude that the mean math SAT score at the school is the same when in fact it is different

Quizplus · Accepted Answer

A Type II error occurs when the null hypothesis ($H_0$) is not rejected when it is false. In this context, it means the teacher would conclude that the mean math SAT score has not changed from 472, when in reality, it has changed (either increased or decreased).

In 2014 , the Average Math SAT Score for Students H0:μ=472HA:μ≠472\begin{array} { l } H _ { 0 } : \mu = 472 \\H _ { A } : \mu \neq 472\end{array}H0​:μ=472HA​:μ=472​

In 2014 , the Average Math SAT Score for Students $\begin{array} { l } H _ { 0 } : \mu = 472 \\H _ { A } : \mu \neq 472\end{array}$