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Cuckoos are known to lay their eggs in the nests of other (host) birds. The eggs are then adopted and hatched by the host birds. A study by E.B. Chance in 1940 in a paper titled “The Truth About the Cuckoo” demonstrated that cuckoos lay their eggs in the nests of a particular host species.Further, cuckoos appear to mate only within their territory. Therefore, geographical sub-species are developed, each with a dominant foster-parent species, and natural selection has ensured the survival of cuckoos most fitted to lay eggs that would be adopted by a particular foster-parent species. The hypothesis is that the mean length of cuckoo eggs depends upon foster-parent species.Data was available for six different foster-parent species (one of which was the wren). A total of 115 observations were made: for each observation, the length of the cuckoo egg in the foster-parent nest was recorded. Analysis was conducted and the mean length of cuckoo eggs for each foster-parent species was compared.The null hypothesis was rejected (p-value<0.05).Assuming the model assumptions were satisfied we can concludeGroup of answer choicesThere is evidence to suggest that the six population means are equal to each otherThere is evidence to suggest that the six sample means are equal to each otherThere is evidence to suggest that each population mean differs significantly from all other population meansThere is evidence to suggest that each sample mean differs significantly from all other sample meansThere is evidence to suggest that some subset of population means differs significantly from some other subset of population meansThere is evidence to suggest that some subset of sample means differs significantly from some other subset of sample means

Question

Cuckoos are known to lay their eggs in the nests of other (host) birds. The eggs are then adopted and hatched by the host birds. A study by E.B. Chance in 1940 in a paper titled “The Truth About the Cuckoo” demonstrated that cuckoos lay their eggs in the nests of a particular host species.Further, cuckoos appear to mate only within their territory. Therefore, geographical sub-species are developed, each with a dominant foster-parent species, and natural selection has ensured the survival of cuckoos most fitted to lay eggs that would be adopted by a particular foster-parent species. The hypothesis is that the mean length of cuckoo eggs depends upon foster-parent species.Data was available for six different foster-parent species (one of which was the wren). A total of 115 observations were made: for each observation, the length of the cuckoo egg in the foster-parent nest was recorded. Analysis was conducted and the mean length of cuckoo eggs for each foster-parent species was compared.The null hypothesis was rejected (p-value<0.05).Assuming the model assumptions were satisfied we can concludeGroup of answer choicesThere is evidence to suggest that the six population means are equal to each otherThere is evidence to suggest that the six sample means are equal to each otherThere is evidence to suggest that each population mean differs significantly from all other population meansThere is evidence to suggest that each sample mean differs significantly from all other sample meansThere is evidence to suggest that some subset of population means differs significantly from some other subset of population meansThere is evidence to suggest that some subset of sample means differs significantly from some other subset of sample means

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Solution

Based on the information provided, the null hypothesis was rejected (p-value<0.05). This means that there is significant evidence to suggest that the mean length of cuckoo eggs does not remain the same across different foster-parent species.

Therefore, the correct answer would be: "There is evidence to suggest that some subset of population means differs significantly from some other subset of population means".

This conclusion is drawn because the rejection of the null hypothesis indicates that not all population means are equal, suggesting that the mean length of cuckoo eggs varies depending on the foster-parent species. However, it does not specify which or how many of the population means differ, hence the use of the term "some subset".

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