An experiment was performed to test the response of rabbit ticks to light. Thirt

Question

An experiment was performed to test the response of rabbit ticks to light. Thirty ticks were placed in the middle of an arena and a light was shown on one side of the arena. If ticks moved toward the light, this was marked as "+" movement; if ticks moved away from the light, this was marked as "-" movement, in response to the light source. Realizing that the size of the arena might have an effect, the procedure was repeated with the same 30 ticks in an arena about twice the size as the first. An equal percentage of + movement was found between the two procedures (i.e., the same percentage of + movement, irrespective of the size of the arena)

A. What is the correct Chi-square value for evaluating the null hypothesis that the probability of + movement is the same in small and large arenas? Answer to the nearest 0.1.

B. Why should the null hypothesis be rejected despite an equal number of + and - movements? Choose the best answer from those below. (More than one might be correct but one is the most correct.)

- Just because an equal number of + and - values were observed, they were not equally distributed within both arena types.   This is true of any dichotomous outcome - an equal number of observations will be observed for two cases.

- Just because an equal number of + and - values were observed, they were not equally distributed within both arena types. Exactly 2/3 of the ticks moved away from the light in the small arena and exactly 2/3 of the ticks moved toward the light in the large arena. So although the total number of + and - movements were equal, they were not equal within arenas. (I.e., 30 ticks total moved toward the light; 20 in the large arena and 10 in the small arena. 30 ticks moved away from the light; 20 in the small arena and 10 in the large arena.)

- It cannot be rejected.

- In the large arena, more ticks moved away from the light; in the small arena, more ticks moved toward the light. Since the same tick were involved in both arenas, one can focus on the ticks that changed behavior. A total of 10 ticks changed behavior; 9 of these ticks moved toward light in the small arena but away from the light in the large arena.

Explanation / Answer

A. The chi-square value is 0.

B. It cannot be rejected.

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