Researchers studying animal behavior have found that rats can quickly learn to play hide-and-seek with humans. The rats seem to love the game, squeaking and jumping for joy when they find the human or are found by the human. The game is played in a large room with multiple boxes. Some of the boxes are transparent and easy to see through, while others are opaque and the inside cannot be seen. Rats go in and out of these boxes and the researchers studied whether they treated the boxes differently depending on whether they were hiding (and didn’t want to be seen) or seeking (and didn’t care if they were seen). For rats who had been learning the game for about a week, the data on the number of times the rats entered the two types of boxes in each situation are shown in Table 2.13.

(a) When rats were hiding, what proportion of the time did they go into opaque boxes? 

(b) When rats were seeking, what proportion of the time did they go into opaque boxes? 

(c) Find the difference and give notation for the difference in sample proportions.

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Table 2.13 Rats know how to hide in hide-and-seek! Hiding Seeking Total Transparent Opaque Total 15 38 53 17 14 31 32 52 84