If a male wants mating success, he should not hang out with hyper-aggressive males. They tend to scare away all the females. At least, that is the message from a study on water striders. Water striders are common bugs that skate across the surface of water. Water striders have different personalities and some of the males are hyper-aggressive, meaning they jump on and wrestle with any other water strider near them. Individually, because hyper-aggressive males are much more active, they tend to have better mating success than more inactive striders. This study examined the effect they have on a group. Four males and three females were put in each of ten pools of water. Half of the groups had a hyper aggressive male as one of the males and half did not. The proportion of time females are in hiding was measured for each of the 10 groups, and a measure of mean mating activity was also measured with higher numbers meaning more mating. Results are shown in Table A.11 and are available in WaterStriders.

Table A.11

(a) For the five groups with no hyper-aggressive male, find the mean and standard deviation of the proportion of time females stay in hiding. Also find the same summary statistics for the five groups with a hyper-aggressive male. Does there seem to be a difference in the proportion of time females are in hiding between the two groups?

(b) Using all 10 data points, make a scatterplot of the proportion of time females are hiding and the mean mating activity. We consider the proportion of time in hiding to be the explanatory variable.

(c) Using all 10 points, find the regression line to predict mean mating activity from the proportion of time females spend hiding.

(d) For each of the two means found in part (a), find the predicted mating activity for that proportion of time in hiding. What is the predicted mean mating activity if there is not a hyper-aggressive male in the group? What is the predicted mean mating activity if there is a hyper-aggressive male in the group?

(e) What advice would you give to a male water strider that wants to mate?

Transcribed Image Text:

Aggressive Male? Females Hiding Mating Activity No 0.48 No 0.48 0.45 No No 0.09 0.30 0.49 No 0.13 Yes 0.16 0.49 0.17 Yes 0.57 0.25 Yes 0.36 0.55 Yes 0.45 Yes 0.82 0.11