An artist experimenting with clay to create pottery with a special texture has b

Question

An artist experimenting with clay to create pottery with a special texture has been experiencing difficulty with these special pieces. Many break in the kiln during firing. Hoping to reduce the amount of pieces that break during firing, she buys some more expensive clay from another supplier. She plans to make and fire 25 pieces and will decide to use the new clay if less than 20% break in the kiln during firing.

a)What would a type II error mean in this context?

A. She does not switch clays when in fact the true proportion of pieces that break during

firing with the expensive clay is less than 20%.
B. She does switch clays when in fact the true proportion of pieces that break during

firing with the expensive clay is less than 20%.
C. She does not switch clays when in fact the true proportion of pieces that break during

firing with the expensive clay is greater than 20%.
D. She does switch clays when in fact the true proportion of pieces that break during

firing with the expensive clay is greater than 20%.

Explanation / Answer

We are testing the claim that the new clay is having less than 20% break in the kiln during firing. So the Type II error will be not rejecting the null hypothesis when it is false. That means:

She does not switch clays when in fact the true proportion of pieces that break during firing with the expensive clay is less than 20%.

Option A is correct.

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