An article discusses the different roles taken by lionesses as they attack and capture prey. The authors were interested in the effect of the position in line as stalking occurs. An individual lioness may be in the center of the line or on the wing (end of the line) as they advance toward their prey. In addition to position, the role of the lioness was also considered. A lioness could initiate a chase (be the first one to charge the prey), or she could participate and join the chase after it has been initiated. Data from the article are summarized in the accompanying table. Position Initiate Chase Participate in Chase Center 27 Role 69 47 Wing (a) Is there evidence of an association between position and role? Test the relevant hypotheses using a = 0.01. State the null and alternative hypotheses. O Ho: Role category proportions are the same for lionesses who are in the center of the line or on the wing. H: Role category proportions are not all the same for lionesses who are in the center of the line or on the wing. 40 O Ho: Position and role are independent. H: Position and role are not independent. OH: Role category proportions are not all the same for lionesses who are in the center of the line or on the wing. H: Role category proportions are the same for lionesses who are in the center of the line or on the wing. O Ho: Position and role are not independent. H: Position and role are independent. Calculate the test statistic. (Round your answer to two decimal places.) What is the P-value for the test? (Use a statistical computer package calculate the P-value. Round your answer to four decimal places.) P-value= What can you conclude? O Do not reject Ho. There is convincing evidence that there is an association between position and role. O Reject Ho. There is convincing evidence that there is an association between position and role. O Do not reject Ho. There is not convincing evidence that there is an association between position and role. O Reject Ho- There is not convincing evidence that there is an association between position and role. (b) What assumptions about how the data were collected must be true for the chi-square test to be an appropriate way to analyze these data? (Select all that apply.) More than 30 of each group were selected for the sample. The data was selected through random sampling. The same number of each group was selected for the sample. The data was selected through convenience sampling. The data was selected through systematic sampling.