A company claims that 20% of their mixed nuts are cashews, 30% are almonds, and the rest are peanuts and that they thoroughly mix millions of nuts and a machine shoots them into packages of 200. In other words, individual packages will vary in their nut distribution just due to random chance. To test their claim I bought a package of their mixed nuts. It contained 200 nuts. I counted 40 cashews, 40 almonds, and 120 peanuts.
1. The null hypothesis is that the observed data fits the model "good". Which of the following best describes the model. In other words what is the null box, how many draws and with or without replacement? In this situation, draw your box for the population, assuming the null hypothesis is true.
The situation does not translate into random draws from a null box because there is no random process involved in the situation we are investigating.
The null box has 200 tickets: 40.00 tickets marked cashews, 60.00 marked almonds, and 100.00 marked peanuts. 200 tickets are randomly drawn without replacement.
The null box has millions of tickets, 20% marked cashews, 30% marked almonds, and 50% marked peanuts. 200 tickets are randomly drawn without replacement.
The null box has 200 tickets: 40 marked cashews, 40 marked almonds, and 120 marked peanuts. 200 tickets are randomly drawn without replacement.
The null box has 10 tickets: 2 tickets marked cashews, 3 marked almonds, and 5 marked peanuts. 200 tickets are randomly drawn with replacement.
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