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. She collected some data, then tested the null hypothesis H₀: µold - µnew = 0 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 not.
D) Deciding that the new lenses are not really cheaper, when in fact they are.
E) Applying these results to all contact lenses, old and new.

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. She collected some data, then tested the null hypothesis H₀: µold - µnew = 0 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 not.
D) Deciding that the new lenses are not really cheaper, when in fact they are.
E) Applying these results to all contact lenses, old and new.

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 corresponds to option D.

A Contact Lens Wearer Read That the Producer of a New