Answer:
A Type II error is when the null hypothesis is failed to be rejected even when the alternative hypothesis is true.
In this case, it would represent that the new program really increases the pass rate, but the sample taken is not enough statistical evidence to prove it. Then, the null hypothesis is not rejected.
The consequence is that the new method would be discarded (or changed) eventhough it is a real improvement.
Step-by-step explanation:
Given that mean=56.1 and standard deviation=8.2, P(x>67.5) will be found as follows:
The z-score is given by:
z=(x-μ)/σ
thus the z-score will be given by:
z=(67.5-56.1)/8.2
z=11.4/8.2
z=1.39
thus
P(z=1.39)=0.9177
thus:
P(x>67.5)=1-P(z>0.9177)
=1-0.9177
=0.0823
Answer: A. 0.0823
