A contact lens wearer read that the producer of a new contact lens boasts that their hypothesis $H _ { 0 } : \mu _ { \text {old } } - \mu _ { \text {new } } = 0$ is tested against the alternative $H _ { A } : \mu _ { \text {old } } - \mu _ { \text {new } } 0$. Which of the following would be a Type II error?
A) Deciding that the new lenses are cheaper, when in fact they really are.
B) Deciding that the new lenses are cheaper, when in fact they are not.
C) Deciding that the new lenses are not really cheaper, when in fact they are.
D) Deciding that the new lenses are not really cheaper, when in fact they are not.
E) It does not matter.

Question

A contact lens wearer read that the producer of a new contact lens boasts that their hypothesis $H _ { 0 } : \mu _ { \text {old } } - \mu _ { \text {new } } = 0$ is tested against the alternative $H _ { A } : \mu _ { \text {old } } - \mu _ { \text {new } } > 0$. Which of the following would be a Type II error?
A) Deciding that the new lenses are cheaper, when in fact they really are.
B) Deciding that the new lenses are cheaper, when in fact they are not.
C) Deciding that the new lenses are not really cheaper, when in fact they are.
D) Deciding that the new lenses are not really cheaper, when in fact they are not.
E) It does not matter.

Quizplus · Accepted Answer

A Type II error is failing to reject a false null hypothesis. In this case, it means deciding that the means of the old and new lenses are the same (not really cheaper), when in fact the new lenses are cheaper (the alternative hypothesis is true). So, option C fits this definition.

A Contact Lens Wearer Read That the Producer of a New