When honeybees are looking for a new home, they send out scouts to explore options. When a scout returns, she does a €˜€˜waggle dance€ with multiple circuit repetitions to tell the swarm about the option she found. The bees then decide between the options and pick the best one. Scientists wanted to find out how honeybees decide which is the best option, so they took a swarm of honeybees to an island with only two possible options for new homes: one of very high honeybee quality and one of low quality. They then kept track of the scouts who visited each option and counted the number of waggle dance circuits each scout bee did when describing the option. Comparative dotplots of number of circuits performed by the 41 bees that visited the high-quality option and the 37 bees that visited the low-quality option are shown in Figure 2.47. The data are available in HoneybeeCircuits.  

Figure 2.47

(a) Does there appear to be an association between number of circuits in the waggle dance and the quality of the site? If so, describe the association.

(b) The five number summary for the number of circuits for those describing the high-quality site is (0, 7.5, 80, 122.5, 440), while the five number summary for those describing the low-quality site is (0, 0, 0, 42.5, 185). Use the IQR method to identify any outliers in either group. Justify your answer.

(c) The mean for the high-quality group is xÌ…_H = 90.5 with a standard deviation of 94.6, while the mean for the low-quality group is xÌ…_L = 30.0 with a standard deviation of 49.4. What is the difference in means, xÌ…_H ˆ’ xÌ…_L?

(d) Find the z-score for the largest value in the high quality group and the z-score for the largest value in the low-quality group. Which is larger relative to its group?

(e) Is it appropriate to use the 95% rule with either set of data?

Transcribed Image Text:

Bococose 200 100 300 400 Clrcults Quality Low High