Rock Sparrows. Rock Sparrows breeding in northern Italy are the subject of a long-term ecology and conservation study due to their wide variety of breeding patterns. Both males and females have a yellow patch on their breasts that is thought to play a significant role in their sexual behavior. A. Pilastro et al. conducted an experiment in which they increased or reduced the size of a female’s breast patch by dying feathers at the edge of a patch and then observed several characteristics of the behavior of the male. Their results were published in the paper “Male Rock Sparrows Adjust Their Breeding Strategy According to Female Ornamentation: Parental or Mating Investment?” (Animal Behaviour,Vol. 66, Issue 2, pp. 265–271). Eight mating pairs were observed in each of three groups: a reduced-patch-size group, a control group, and an enlarged-patch-size group. The data on the WeissStats site, based on the results reported by the researchers, give the number of minutes per hour that males sang in the vicinity of the nest after the patch size manipulation was done on the females. At the 1% significance level, do the data provide sufficient evidence to conclude that a difference exists in the mean singing rates among male Rock Sparrows exposed to the three types of breast treatments? a. conduct a one-way ANOVA test on the data. b. interpret your results from part (a). c. decide whether presuming that the assumptions of normal populations and equal population standard deviations are met is reasonable.

Rock Sparrows. Rock Sparrows breeding in northern Italy are the subject of a long-term ecology and conservation study due to their wide variety of breeding patterns. Both males and females have a yellow patch on their breasts that is thought to play a significant role in their sexual behavior. A. Pilastro et al. conducted an experiment in which they increased or reduced the size of a female’s breast patch by dying feathers at the edge of a patch and then observed several characteristics of the behavior of the male. Their results were published in the paper “Male Rock Sparrows Adjust Their Breeding Strategy According to Female Ornamentation: Parental or Mating Investment?” (Animal Behaviour,Vol. 66, Issue 2, pp. 265–271). Eight mating pairs were observed in each of three groups: a reduced-patch-size group, a control group, and an enlarged-patch-size group. The data on the WeissStats site, based on the results reported by the researchers, give the number of minutes per hour that males sang in the vicinity of the nest after the patch size manipulation was done on the females. At the 1% significance level, do the data provide sufficient evidence to conclude that a difference exists in the mean singing rates among male Rock Sparrows exposed to the three types of breast treatments?

a. conduct a one-way ANOVA test on the data.

b. interpret your results from part (a).

c. decide whether presuming that the assumptions of normal populations and equal population standard deviations are met is reasonable.