Do female models have eye colors that are distributed differently than those of the population of their country? That is a question that UK researchers were interested in exploring (Forti, 2016). They sampled from 400 profiles of females registered as commercial models in the United Kingdom and found that 187 had blue eyes, 120 had brown eyes, and 93 other colors. They reported that another study showed that 71.5% of female UK residents are thought to have blue eyes, 21% have brown eyes, and 7.5% other colors. 

a. What are the expected frequencies for each eye color of the 400 models, assuming the eye colors are distributed in the same way as those of all female UK residents? 

b. Write out the hypotheses. 

c. Calculate the test statistic and appropriate p-value. 

d. State your conclusion in the context of the research question.