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 more expensive, when in fact they are cheaper.
B) Deciding that, on average, the new lenses are cheaper, when in fact they are not.
C) Deciding that, on average, the new lenses are not really cheaper, when in fact they are.
D) Deciding that the prices of new lenses are exactly the same as the old ones, when in fact they are not.
E) Deciding that the prices of old lenses are exactly the same as the new ones, when in fact they are not.

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 more expensive, when in fact they are cheaper.
B) Deciding that, on average, the new lenses are cheaper, when in fact they are not.
C) Deciding that, on average, the new lenses are not really cheaper, when in fact they are.
D) Deciding that the prices of new lenses are exactly the same as the old ones, when in fact they are not.
E) Deciding that the prices of old lenses are exactly the same as the new ones, when in fact they are not.

Quizplus · Accepted Answer

A Type II error occurs when the null hypothesis is not rejected when it is false. In this context, it means failing to detect that the new lenses are cheaper when they actually are, which aligns with option C.

A Contact Lens Wearer Read That the Producer of a New