A model in herding cats results in cats herding easily, herding mostly in the ri

Question

A model in herding cats results in cats herding easily, herding mostly in the right direction, and not herding at all. Based on previous experiments, the proportion of cats that herd easily should be about .05, those that herd mostly in the right direction should be about .15, and those that just will not herd at all about .80. In the most recent experiment, conducted with 82 randomly selected cats, about 8 of cats herded easily, 12 herded mostly in the right direction, and 62 did not herd at all. Carry out a test to determine whether the previous cat herding model seems to hold in this setting.

Explanation / Answer

Hypotheses:   

Ho: The distribution is as per the expectation   

Ha: The distribution is not as per the expectation; that is, it is different   

Decision Rule:   

= 0.05

Count = 3

Degrees of freedom =   3 - 1 = 2

Critical Value of 2 = 5.991464547

Reject Ho if 2 > 5.991464547

Decision (in terms of the hypotheses):    

Since 3.914634146 < 5.991464547 we do not reject Ho

Conclusion (in terms of the problem):    

There is no sufficient evidence that the distribution is different    

Test Statistic: Recorded Expected (Recorded - Expected)^2 / Expected 8 4.1 3.709756098 12 12.3 0.007317073 62 65.6 0.197560976 2 = 3.914634146 2 = 3.914634146 p- value = 0.141236841

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