A contact lens wearer read that the producer of a new contact lens boasts that their
Lenses are cheaper than contact lenses from another popular company. The null 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
Lenses are cheaper than contact lenses from another popular company. The null 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 occurs when the null hypothesis is not rejected when it is actually false. In this context, it means deciding that the new lenses are not cheaper when they actually are.

A Contact Lens Wearer Read That the Producer of a New