Chapter 9.5, Problem 2Q

Male fiddler crabs solicit attention from the opposite sex by standing in front of their burrows and waving their claws at the females who walk by. If a female likes what she sees, she pays the male a brief visit in his burrow. If everything goes well and the crustacean chemistry clicks, she will stay a little longer and mate. In what may be a ploy to lessen the risk of spending the night alone, some of the males build elaborate mud domes over their burrows. Do the following data $\left(229\right)$ suggest that a male’s time spent waving to females is influenced by whether his burrow has a dome? Answer the question by constructing and interpreting a 95% confidence interval for ${\mu }_X-{\mu }_Y$. Use the value $s_p=11.2$.

% of Time Spent Waving to Females
Males with Domes, $x_i$	Males without Domes, $y_i$
100.0	76.4
58.6	84.2
93.5	96.5
83.6	88.8
84.1	85.3
	79.1
	83.6