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 H0: μold -μnew = 0 is tested against the alternative HA: μold -μnew 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 H0: μold -μnew = 0 is tested against the alternative HA: μold -μnew > 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 made when the null hypothesis is not rejected when it should have been rejected. In this case, the null hypothesis is that the mean cost of the old contact lens is the same as the mean cost of the new contact lens. If the decision is made that the new lenses are not really cheaper when in fact they are, the null hypothesis is not rejected when it should have been, resulting in a Type II error.

A Contact Lens Wearer Read That the Producer of a New