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 t 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 Center Wing Initiate Chase Participate in Chase 26 Role 67 46 43 (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: Position and role are independent. H₂: Position and role are not independent. O Ho: Role category proportions are the same for lionesses who are in the center of the line or on the wing. H₂: Role category proportions are not all the same for lionesses who are in the center of the line or on the wing. O Ho: 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.) x² = What is the P-value for the test? (Use a statistical computer package to calculate the P-value. Round your answer to four decimal places.) P-value = What can you conclude? 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 Do not reject Ho. There is 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.) The data was selected through systematic sampling. More than 30 of each group were selected for the sample. The data was selected through random sampling. The data was selected through convenience sampling. The same number of each group was selected for the sample.

If the points (h, 0), (a, b), and (0, k) lie on a line, show that 1 + k h

A hiker is returning to a campsite that is 5 miles east and 2 miles south fromtheir current position. The hiker is currently walking east along a path at a pace of 4 milesper hour. The hiker plans to leave the path and walk in a straight line diagonally towardsthe cabin through the woods. The hiker can only walk at a pace of 3 miles per hour throughthe woods. Where should the hiker leave the path and turn into the woods if they want toget to the campsite as quickly as possible?

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 Center Wing Initiate Chase Participate in Chase 28 Role 69 O Ho: Position and role are not independent. H₂: Position and role are independent. 49 (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 not all the same for lionesses who are in the center of the line or on…

ans. and 7) show that the lines リ-3 メ-2 = -2 2ー3 メー2-4 intersect. X-2 = %3D 2

Rewrite the equations in the form y=mx + c and then determine the y-intercept and gradient of each graph......A, B ,C,D,E,F

Find the equation of the line which best fits the data points (2;1) , (4;4), (5;1),(6;3).