Question

For alligators caught in two lakes, the accompanying table shows their primary food choice. The four food categories refer to fish, invertebrates (such as snails, insects, or crayfish), birds and reptiles (such as egrets or turtles), and others, including mammals or plants. Is there evidence that primary food choice differs between the two lakes? Complete parts a through d below EEBClick the icon to view the alligator food choice data a. Find the conditional sample distributions of primary food choice in lakes A and B X Alligator Food Choices Lake Birds & Reptiles Fish Invertebrates Others 7 % 34 % 52 % 25 % 16 % A 18 % 24 % 24 % В Primary Food Birds & Reptiles (Round to the nearest integer as needed.) Lake Fish Invertebrates Others A 29 4 9 14 56 b. Set up the hypotheses of interest. B 12 17 12 9 50 Ho Lake and food source are independent. Ha Lake and food source are dependent Print Done c. The X2-value for this table equals 16.32. Based on the df for the corresponding chi-squared distribution, can thiis be considered large? Why? This X2-value is standard deviations away from the mean extreme because it is (Round to two decimal places as needed.) d. The P-value for the chi-squared test is 0.001. Write the conclusion of the test in context Ho There is not sufficient evidence to conclude that lake and food source are independent Reject

Answer 1

(a)

Conditional Sampling distributions of primary food choices in lakes A and B:

Lake	Fish	Invertebrates	Birds & Reptiles	Others
A	29/56=0.5179	4/56=0.0714	9/56=0.1607	14/56=0.25
B	12/50=0.24	17/50=034	12/50=0.24	9/50=0.18

(b)

H0	Lake and food source are independent
H1	Lake and food source are dependent

(c)

Degrees of Freedom = (r - 1) X (c - 1)

                            = (2 - 1) X (4 - 1)

                            = 3

Mean of $\chi ^{2}$ Distribution = Degrees of Freedom = 3

Standard Deviation of $\chi ^{2}$ Distribution =

V2 x 3= V6 = 2.4495

Given:

Calculated value of $\chi ^{2}$ = 16.32

So, we get:

(16.32 - 3)/2.4495 = 5.4378

So,

Answer is:

This $\chi ^{2}$ - value is extreme because it is 5.4378 standard deviations away from mean 3.

(d)

Given:

p value = 0.001

So,

Correct option:

Reject H0. There is sufficient evidence to conclude that Lake and food source are dependent