Quality control. A farmer is claiming that the apples he produces are categorized, according to their size, as small, medium, and large and that the percentages of each category are: 25% small, 45% medium, and 30% large apples.

You collect the production of some trees and separate the various categories. You find that there are 55 kg of small apples, 120 kg of medium apples, and 85 kg of large apples. You wonder whether your mix is significantly different from what the farmer is claiming.

a) Can we use a chi-square goodness-of-fit test to check the farmer’s claim?

b) How can we change the experiment in order to use a x2 test?