Captivity can influence immunological responses in some mammals. Seeber et al. (2020) investigated various aspects of immunological responses in captive and free-ranging zebras. One aspect of the study involved samples of 12 free-ranging zebras from Namibia, 9 from Tanzania, and 38 captive zebras from various zoos in Europe. (All of these were non-lactating females.) One of the measured variables from blood samples was lysozyme concentration (μg/L). (Lysozyme is a biomarker of the immune response.) The researchers were interested in investigating possible differences in lysozyme concentration between zebras in the various locations.  As part of the analysis, they carried out a one-way ANOVA on the lysozyme concentrations for the zebras from the 3 locations, and found the following output.                    Df  Sum Sq    Mean Sq   F value   Pr(>F)     Location     2    50.65      25.33        42.24     6.54e-12 Residuals   56   33.57      0.60  Suppose the assumptions of one-way ANOVA are reasonable here.  (For the purposes of this question, ignore any possible issues such as outliers or skewness.) Give a conclusion to the ANOVA F test that relates to the situation at hand.  Also, suggest a path forward for the researchers. (What sort of analysis can they do to further explore this data?)

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Captivity can influence immunological responses in some mammals. Seeber et al. (2020) investigated various aspects of immunological responses in captive and free-ranging zebras. One aspect of the study involved samples of 12 free-ranging zebras from Namibia, 9 from Tanzania, and 38 captive zebras from various zoos in Europe. (All of these were non-lactating females.) One of the measured variables from blood samples was lysozyme concentration (μg/L). (Lysozyme is a biomarker of the immune response.)

The researchers were interested in investigating possible differences in lysozyme concentration between zebras in the various locations.  As part of the analysis, they carried out a one-way ANOVA on the lysozyme concentrations for the zebras from the 3 locations, and found the following output.

                   Df  Sum Sq    Mean Sq   F value   Pr(>F)    
Location     2    50.65      25.33        42.24     6.54e-12
Residuals   56   33.57      0.60 

Suppose the assumptions of one-way ANOVA are reasonable here.  (For the purposes of this question, ignore any possible issues such as outliers or skewness.)

Give a conclusion to the ANOVA F test that relates to the situation at hand. 

Also, suggest a path forward for the researchers. (What sort of analysis can they do to further explore this data?)  

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